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The cylindrical -- conical intersections are often met in technique as parts of pipes, tanks, bends etc. The paper work proposes a comparison between methods to solve the cylindrical -- conical intersection problems. The problems may be solved either applying graphical, descriptive geometry methods or using analytical methods. The graphical method uses a certain number of points to find the intersection curves and the development of the solids, the analytical method uses a complex enough mathematical apparatus. [ABSTRACT FROM AUTHOR]

In this paper we consider second order iterative boundary value problem with Sturm Liouville type boundary conditions and establish the existence of countably many positive symmetric solutions by using Krasnoselskii's fixed point theorem for operator on a cone. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of radial solutions to a k-Hessian system in a general form. The existence of radial solutions is obtained under the assumptions that the nonlinearities in the given system satisfy k-superlinear, k-sublinear or k-asymptotically linear at the origin and infinity, respectively. The results presented in this paper generalize some known results. Examples are given for the illustration of the main results. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵ 2 u = f (u , ▵ u) on an annular domain Ω in R N with the Navier boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : R + × R − → R + is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f (ξ , η) to have superlinear or sublinear growth on ξ , η as | (ξ , η) | → 0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C([0, 1] × R+n × Rn × Rn × Rn, Rn) considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish new existence criterion that ensure the existence of at least one and the existence of at least two nonnegative solutions. [ABSTRACT FROM AUTHOR]

This paper attempts to investigate the existence of at least one positive solution and the existence of a unique positive solution to an iterative and conformable fractional system associated with the Sturm–Liouville type conditions. The approach employed in this work relies on the well-known Guo–Krasnosel'skii fixed point theorem and Wardowski fixed point theorem. To ensure the validity of our key findings, examples are included. [ABSTRACT FROM AUTHOR]

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined. [ABSTRACT FROM AUTHOR]

This paper examines the thermal transfer attributes of ZnO-H2O Walter's-B nanoliquid flow alongside an upright cone in the bearing of slip mechanism, radiative heat flux, and non-uniform heat source. We adopted suitable similarities to convert the nonlinear PDEs into ODEs and solved the transformed governing system by employing the bvp5c solver package in Matlab software. The prime novelty of this research is to compute the effective thermal diffusivity of the nanoliquid via the Maxwell and Xue nanomodels. Further, simultaneous results are deliberated for Maxwell and Xue cases via pictorial outcomes under various controlling limitations, such as velocity slip, radiative heat flux, buoyancy, viscoelastic, and volume fraction of nanomaterial. The thermal transmission rate of nanoliquid reported by the Xue nanomodel is higher than the Maxwell nanomodel. Therefore, the Xue nanomodel effectively works to enhance the thermal conductivity of the liquids with viscoelastic nature. Further, this study is helpful in industrial processing, where control over heat transport is required. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of multiple positive solutions for a class of φ-Laplacian boundary value problem with a nonlinear fractional differential equation and fractional boundary conditions. Multiple solutions are proved under slight conditions on a possibly degenerating source term. Approximation techniques together with the fixed point index theory a on cone of a Banach space are employed. Some illustrating examples of are also supplied. [ABSTRACT FROM AUTHOR]

This paper will argue that Whiteness must be addressed within White contexts as a challenge to the prevalent colour-blindness, which distorts our imaginative horizons and presents a warped gospel aesthetic. In other words, Whites like myself need to use our agency to reckon with and repent of Whiteness at the behest of our Black sisters and brothers. Otherwise, attempts to appropriate lament into corporate worship will be reduced to voyeurism, individualism and consumerism. I will mainly interact with James Cone and Anthony Reddie, both of whom critique the way Black suffering can become overlooked or usurped. Within the paper, some tentative suggestions will be made on how to proceed with appropriating lament into corporate worship, lest our theology and practices unwittingly (or intentionally) bury those who suffer beneath the veneer of false peace and colour-blindness. [ABSTRACT FROM AUTHOR]

This work continues a series of author's papers devoted to the problems of the existence and uniqueness of positive solutions of boundary value problems for nonlinear second order functional-differential equations. We study a boundary value problem for a nonlinear second order functional-differential equation with homogeneous boundary conditions. Based on the theory of semi-ordered spaces and with the help of special topological tools we establish the existence of a unique positive solution to the problem. [ABSTRACT FROM AUTHOR]

In the paper, we consider a boundary value problem for a second order functional-differential equation with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces and with the help of special topological methods, we prove the existence of a unique positive solution to the problem. [ABSTRACT FROM AUTHOR]

In this paper, we build four-part cone models to explore the coupling effect of seven cone fiber couplers. Moreover, this is the first study of the coupling effect of four layers of biological couplers in animals and other biological lives. We simulate the four layers cone couplers by using the beam propagation method, and we assume the input beam is located at the outer fiber of the central cone. Our simulation results showed that there are two wavelength regions (short and long wavelength regions) with the strongest coupling, where the most power of input optical powers of the central cones will transfer to the six surrounding cones after transmitting through the four layers of cone couplers. However, within a wavelength region of ±75 nm near to the peak wavelengths, located in the yellow–green wavelength range, the splitting ratios at the output of the outer segment of the central cone are always greater than the sum of the splitting ratios of the six surrounding cones. These cone couplers may play an important role in color preprocessing (e.g., doing opponent color processing partially). The cone fiber coupler effect and light absorption of cones are considered separately in our models. By taking account of both the cone fiber coupling effect and absorption of outer segment of L cone, we find the multiplication of the relative optical power of cone couplers, the spectral sensitivity data of the L cone, and a normalized coefficient that matches with the photopic luminous efficiency of the human eye well. This is the attempt to use both the cone fiber coupling effect and the absorption of L cones to explain the photopic luminous efficiency. The splitting ratios of the central cones are greater than 80% at peak wavelengths located in the yellow-green wavelength range, and this can help to explain why the human eye is more sensitive to green light. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional impulsive wave equations and improves a previous results. In fact, this paper adopts a new topological approach to prove the existence of classical solutions with a complex arguments caused by impulsive perturbations. To the best of our knowledge, there is a severe lack of results related to such impulsive equations. [ABSTRACT FROM AUTHOR]

In this paper we present some theorems on the multiplicity of fixed points of some operators on a special wedge and using these results we consider x ″ + f (t , x , x ′) = 0 , t ∈ (0 , 1) x (0) = 0 , x (1) = 0 and establish the existence of multiple solutions. [ABSTRACT FROM AUTHOR]

This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground set of the objective relation). Several characterizations are formulated that express undominated maximals of an objective relation as maximals of some trace associated with that objective relation. By means of some of these characterizations, the structure of the entire set of undominated maximals is examined in the particular case of relations induced by open and closed convex cones—among them, the weak and strong Pareto dominance—and, in the case of semiorders, that admit certain types of representability. The results of the last part of the examination allow the construction of many examples of relations whose entire sets of maximals and undominated maximals are completely identifiable in an elementary way. [ABSTRACT FROM AUTHOR]

The paper presents the results of a numerical study of gas dynamics and integral parameters of the flow at the channel entrance located behind a conical or plane shock wave. The freestream Mach number range is M = 2–4 and the range of the angles of the compression surfaces of the wedge and cone is δ= 10–90°. Data on the flow structure at the channel entrance, mass-averaged Mach numbers, total pressure loss coefficient, and flow rate coefficients are obtained. A comparative analysis of these parameters is performed, and the advantages and drawbacks of the channel entrance positions in various types of the flow are noted. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of at least one solution and at least two nonnegative solutions of impulsive differential equations with the two-point integral boundary conditions. We employ the recent fixed point theorems for the sum of two operators on Banach spaces. The applicability of the results is illustrated through an example. [ABSTRACT FROM AUTHOR]

In this paper, by using the Leggett–Williams fixed-point theorem, we study the existence of positive solutions to fractional differential equations with mixed Riemann–Liouville and quantum fractional derivatives. To prove the effectiveness of our main result, we investigate an interesting example. [ABSTRACT FROM AUTHOR]

The paper considers a two-point boundary value problem with homogeneous boundary conditions for a single 4nth-order nonlinear ordinary differential equation. Using the well-known Krasnoselskii theorem on the expansion (compression) of a cone, sufficient conditions for the existence of a positive solution to the problem under consideration are obtained. To prove the uniqueness of a positive solution, the principle of compressed operators was invoked. In conclusion, an example is given that illustrates the fulfillment of the obtained sufficient conditions for the unique solvability of the problem under study. [ABSTRACT FROM AUTHOR]

It is a well-known fact that there exists a standard minimal embedding map for the Grassmannians of n-planes G (n , m ; F) (F = R , C , H) and Cayley plane O P 2 into Euclidean spheres, then a natural question is that if the cones over these embedded Grassmannians are area-minimizing? In this paper, detailed descriptions for this embedding map are given from the point of view of Hermitian orthogonal projectors which can be seen as a direct generalization of Gary R. Lawlor’s([23]) original considerations for the case of real projective spaces, then we re-prove the area-minimization of those cones which was gradually obtained in [18-19], and [30] from the perspectives of isolated orbits of adjoint actions or canonical embedding of symmetric R-spaces, all based on the method of Gary R. Lawlor’s Curvature Criterion. Additionally, area-minimizing cones over almost all common Grassmannians have been given by Takahiro Kanno, except those cones over oriented real Grassmannians G ~ (n , m ; R) which are not Grassmannians of oriented 2-planes. The second part of this paper is devoted to complement this result, a natural and key observation is that the oriented real Grassmannians can be considered as unit simple vectors in the exterior vector spaces, we prove that all their cones are area-minimizing except G ~ (2 , 4 ; R) . [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of initial boundary value problems for a class of the Kawahara equation. We prove existence of at least one solution and existence of at least one nonnegative solution. The arguments are based upon of recent theoretical results. [ABSTRACT FROM AUTHOR]

This paper interrogates critical divergence in interpreting the cross and atonement between James Cone and Karl Barth – and their related ethics. Cone rejects atonement theories and embraces the cross as an interpretative symbol that speaks to the suffering of Black Americans. In contrast, Barth resists interpreting the cross as a symbol and refuses to interpret the cross separately from the atonement. These divergences lead to different conceptions of sin, salvation, and ethical response. Despite their dissimilarities, I argue that Cone and Barth demonstrate a surprisingly similar kind of ambiguity when it comes to ontology and ethics: Cone blurs ontological Blackness and symbolic Blackness while Barth emphasizes divine ontology in a manner that makes it difficult to address of the material, post-colonial world. I conclude, by demonstrating how these ambiguities in both thinkers create challenges to the concrete addressing of ethical concerns, such as reparations in today's world. [ABSTRACT FROM AUTHOR]

The fixed point theorem of Guo–Krasnosel'skii is applied in this paper to find the intervals of the parameters that have a positive solution to an iterative system of nth order fractional differential equation with three-point boundary conditions including a nonhomogeneous term. [ABSTRACT FROM AUTHOR]

This paper considers the following Dirichlet boundary value problem of the k-Hessian equation: S k σ D 2 z = λ b (| x |) φ (- z) , in Ω , z = 0 , on ∂ Ω , where λ > 0 , Ω stands for the open unit ball in R N , 1 ≤ k ≤ N is an integer, and S k σ D 2 z is the k-Hessian operator of z. We obtain the existence results of k-convex radial solutions of the k-Hessian problem for λ belonging to an open interval. Our main approach is the Guo–Krasnosel'skii fixed point theorem in a cone. [ABSTRACT FROM AUTHOR]

The information about main results on geometry of developable surfaces with an edge of regression which have a directrix ellipse in the base is gathered. These surfaces constitute a group called “Ruled surfaces of conical type on elliptical base”. This group includes elliptical cones, torses with two ellipses defined in the parallel planes, equal slope surfaces, and ruled surfaces with the main frame of three superellipses that are ellipses in one coordinate plane and broken straight lines in the other two coordinate planes. The paper presents a method for developing torses onto a plane, approximation of torses by folded surfaces, and parabolic ending of a thin sheet from elastic material into a torse shell. A brief review of the methods of stress-strain and buckling analysis of the considered ruled shells is given, including the displacement-based finite element method and variational energy method. It is shown that analytical methods can be used only in the case of applying the momentless shell theory for ruled thin shells of conical type. The analytical formulae for determining the normal and tangent internal forces in any momentless conic shell with a superellipse in the base are derived. References to forty four scientific articles of other authors, working or having worked on the subject of the paper are given. These references confirm the conclusions of the author and the perspectives of investigations of the considered ruled surfaces and shells.

We consider the solutions of the Klein–Gordon equation in the 2 + 1 -dimensional space-time which gravity is analyzed, i.e., the manifold ℝ t × ℝ + × ℝ / 2 ⁢ π ⁢ α ⁢ ℤ created by a massive point particle. Using the Schwartz kernel of resolvent and spectral measure for Schrödinger operator on the spinless cone, we prove the dispersive estimates and Strichartz estimates for the Klein–Gordon equation. In a future paper, we will consider the problem on the spinning cone. [ABSTRACT FROM AUTHOR]

We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiı-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

The current study investigates to characterize the Complex Programming Problem (CPP) solution in a fuzzy environment. The paper is divided into two parts: 1) the first presents a Fuzzy Complex Programming Problem (FCPP) with fuzzy complex constraints, and 2) the second presents the optimality criteria using the fuzzy complex cone. The CPP is suggested by involving fuzzy numbers in the constraints in parts. Using the α -cut set concepts, the problem is converted into the α -complex programming. A number of basic theorems with proofs are established concerning the basic results for the fuzzy complex set of solutions for the F-CPP, and the optimality criteria of the saddle point for F-CPP with fuzzy cones is derived. [ABSTRACT FROM AUTHOR]

In this paper we consider a iterative system of two-point boundary value problems with integral boundary conditions having n singularities and involve an increasing homeomorphism, positive homomorphism operator. By applying Hölder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space, we derive sufficient conditions for the existence of denumerably many positive solutions. Finally we provide an example to check validity of our obtained results. [ABSTRACT FROM AUTHOR]

The movement of microorganism cells in fluid influences various biotic processes, including septicity and marine life ecology. Many organic and medicinal applications need to look into the insight of mechanism in nanofluids containing a microbial suspension. The current paper concerns the bioconvection of a ternary hybrid nanofluid (Al2O3-Cu-CNT/water) flow containing motile gyrotactic microorganisms toward three different geometries (a flat plate, a wedge, and a cone) in the occurrence of natural convection, radiation, and heat source/sink. The Cattaneo–Christov theory is employed to develop the model. The equations are solved by using the "bvp4c function in MATLAB". The influence of the crucial significant factors on the motile microorganisms' density, velocity, temperature, nanoparticles' concentration, microbe density gradient, and transmission rates of heat and mass is discussed. The results depict that the heat transmission rate is highest for the flow toward the cone, whereas the mass transmission rate and microbe density gradient are highest for the flow toward the wedge. In addition, the higher estimates of the thermal relaxation parameter corresponding to the Cattaneo–Christov theory act to enhance the rate of heat transmission. The results of the current study will be useful to many microbial-enhanced oil recovery systems, carriage processes, architectural design systems, medicinal fields that utilize nanofluids, and so on. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider the non-separated boundary value problem for system of nonlinear Riemann–Liouville fractional differential equations D 0 + α x (t) + λ f (t , x (t) , y (t)) = 0 , 0 < t < 1 , D 0 + α y (t) + μ g (t , x (t) , y (t)) = 0 , 0 < t < 1 , subject to the boundary conditions x (0) = y (0) = 0 , u 1 D 0 + β x (1) = v 1 D 0 + β y (ξ) , u 2 D 0 + β y (1) = v 2 D 0 + β x (η) , η , ξ ∈ (0 , 1) , where the coefficients u i , v i , i = 1 , 2 are real positive constants, we give sufficient conditions on λ , μ , f and g such that the system has no positive solutions. An example is given to demonstrate the main result. [ABSTRACT FROM AUTHOR]

The precise three-dimensional measurement of fuel nozzles is of great significance to assess the manufacturing accuracy and improve the spray and atomization performance. This paper proposes an improved fast shape from focus (SFF) method for three-dimensional measurement of key features of fuel nozzles. In order to ensure the measurement accuracy and efficiency of the SFF, the dispersion of the measured points from a standard flat plane was used to select the optimal combination of the focus measure operator, window size and sampling step size. In addition, an approximate method for the focus measure interval is proposed to improve the measurement efficiency, which uses the peak region of the central pixel to replace the peak region of other pixels. The results show that the proposed method decreased the average computation time of the focus measure by 79.19% for the cone section and by 38.30% for the swirl slot. Compared with a reference laser scanning microscope, the measurement error in length is within 10 μm and the error in angle is within a maximum 0.15°. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dual cone in Hilbert spaces. We first discuss the relation between the isotonicity of the projection onto the cone and its dual cone. Some sufficient conditions for the isotonicity of the projection with respect to the mutually dual orders onto general cones are then proved. By using the self-dual cone in the hyperplane, we establish some specific isotone projection cones. Some properties and representations of the projection onto these cones are studied. We also prove some heredity and expansivity for the isotonicity of the projection onto these cones. By using the isotonicity characterizations of the projection with respect to the mutually dual orders, some solvability and approximation theorems for the complementarity and conic optimization problems are obtained. In Theorems 5.1–5.4, if the order relation does not satisfy the regularity, to guarantee convergence of isotone Picard iterations, three different order methods are used, respectively. Our results generalize those about the isotone projection cone and methods to establish isotone iterations for complementarity problems. [ABSTRACT FROM AUTHOR]

The electro-hydraulic plastic deforming method belongs to non-conventional plastic deforming techniques class. The shape of the discharging chamber and of the energy concentrators influences workpiece machining, along with the other parameters of the equipment (electrical pulses, electrodes, space between electrodes, pressure wave transmission medium, way to propagate the pressure wave). The paper proposes a comparative analysis of the geometric parameters of the discharging chambers and of their effects on the technological processing. [ABSTRACT FROM AUTHOR]

In this paper, the notion of a fuzzy geometric space is introduced. Some structures related to it are studied and connections of them are investigated. By using fuzzy blocks of a fuzzy geometric space, the concept of strongly transitivity of fuzzy geometric spaces is defined and studied. Finally, it is proved that the relation β is transitive on fuzzy hypergroups, by associating strongly transitivity fuzzy geometric spaces to fuzzy hypergroups. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive solutions of the fully fourth-order boundary value pqroblem u (4) = f (t , u , u ′ , u ″ , u ‴) on [ 0 , 1 ] with the boundary condition u (0) = u (1) = u ″ (0) = u ″ (1) = 0 , which models a statically bending elastic beam whose two ends are simply supported, where f : [ 0 , 1 ] × R + × R × R − × R → R + is continuous. Some precise inequality conditions on f guaranteeing the existence of positive solutions are presented. The inequality conditions allow that f (t , u , v , w , z) may be asymptotically linear, superlinear, or sublinear on u , v , w , and z as | (u , v , w , z) | → 0 and | (u , v , w , z) | → ∞ . Our discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear system of higher order three-point boundary value problems on time scales. The Schauder fixed point theorem is used to investigate the existence of solutions of nonlinear dynamic systems on time scales. Furthermore, we establish the criteria for the existence of at least one, two and three positive solutions for higher order nonlinear dynamic systems on time scales by using the four functionals fixed point theorem, the Avery-Henderson fixed point theorem and the five functionals fixed point theorem, respectively. [ABSTRACT FROM AUTHOR]

Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other novel methods are proposed. The idea of cone constraint provides a new way of solving this problem. However, these approaches do not always perform well and are away from the Cramer-Rao-Lower-Bound (CRLB) in the situations when the source is set at the array edge, the noise in measurement is loud, or the initial position is biased. This paper presents a weighted-least-squares (WLS) algorithm with the cone tangent plane constraint for hyperbolic positioning. The method adds the range between the source and the reference sensor as a dimension. So, the space-range frame is established. Different from other cone theories, this paper sets the reference sensor as the apex and finds the optimal source estimation on the cone. WLS is used for the optimal result from the measurement plane equations, a vertical constraint and a cone constraint. The cone constraint equation is linearized by a tangent plane. This method iterates through loops and updates the tangent plane, which approximates the truth-value on the cone. The proposed algorithm was simulated and verified under various conditions of different source positions and noises. Besides, some state-of-the-art algorithms were compared in these simulations. The results show that this algorithm is accurate and robust under poor external environment. [ABSTRACT FROM AUTHOR]

In this paper we investigate a class of impulsive wave equations. We prove existence of classical solutions for the considered class of equations. A new topological approach is applied to prove the existence of solutions. The arguments are based upon of a recent theoretical result. To the best of our knowledge, there is hardly any work dealing with such impulsive wave. The reason may be the complex arguments caused by impulsive perturbations. [ABSTRACT FROM AUTHOR]

In the present paper, we establish some fixed point theorems in partial cone metric space using certain contractive type conditions. Also we obtain the well known Banach contraction principle, Kannan contraction, Chatterjae contraction and Reich contraction as corollaries to our results in partial cone metric space. Our results extend and generalize several results from the current existing literature. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a generalized nonlinear discrete hematopoiesis model with delays. By applying mixed monotone operator fixed point theorem in an appropriate cone, we discuss the existence and uniqueness of positive almost periodic solution to this model. Four cases are classified based on parameters of the concerned model. The main results provided in the paper are more general than that of some previously known results, which are extended and complemented. Two particular examples are provided to illustrate that the obtained results, which are reasonable. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and nonexistence of positive radial solutions of the elliptic equation − Δ u = f (| x | , u) , u ∈ Ω , u | ∂ Ω = 0 , where Ω = { x ∈ R N : r 1 < | x | < r 2 } , N ≥ 3 and f ∈ C ([ r 1 , r 2 ] × R +) , whose sign may change. We present new eigenvalue criteria for the existence and nonexistence to this problem. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the following second-order coupled differential system with coupled integral boundary value conditions and nonlinearities depending on the first derivatives: - u ″ (t) = f 1 t , u (t) , v (t) , u ′ (t) , v ′ (t) , t ∈ [ 0 , 1 ] , - v ″ (t) = f 2 t , u (t) , v (t) , u ′ (t) , v ′ (t) , t ∈ [ 0 , 1 ] , u (0) = α [ v ] , u ′ (1) = β [ u ] , v (0) = β [ u ] , v ′ (1) = α [ v ] , where α and β denote linear functionals given by α [ u ] = ∫ 0 1 u (t) d A (t) , β [ u ] = ∫ 0 1 u (t) d B (t) involving Stieltjes integrals with suitable functions A, B of bounded variation. By the theory of fixed point index on a special cone in C 1 [ 0 , 1 ] × C 1 [ 0 , 1 ] , the existence of the positive solutions of the system is obtained through posing some inequality conditions and the spectral radius conditions on the nonlinearities. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions for the nonlinear model of the Antarctic Circumpolar Current and analyze their Ulam-Hyers stability. By introducing some conditions on the ocean nonlinear vorticity function depending on other functions and initial values, we establish sufficient conditions to guarantee the existence, multiplicity, location and construction of positive solutions via the approach of fixed point theorem in cones, upper and lower solutions, and monotone method, respectively. Finally, we show the existence and uniqueness and Ulam-Hyers stability of positive solutions when the ocean nonlinear vorticity function has uniformly Lipschitz continuity. [ABSTRACT FROM AUTHOR]