Search

In this paper, we discuss the existence of nonnegative solutions to a fourth order singular boundary value problem at two points. Our result is based on a recent Birkhoff-Kellogg type fixed point theorem developed on translates of a cone on a Banach space. [ABSTRACT FROM AUTHOR]

Using the fixed point theorem in partially ordered sets, we obtain sufficient conditions for the existence of a unique positive solution to a boundary-value problem of the Sturm–Liouville type for a nonlinear ordinary differential equation, and give an example illustrating the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we develop some new multiple fixed point theorems for the sum of two operators T + S where I - T is Lipschitz invertible and S is a k-set contraction on translate of a cone in a Banach space. New existence criteria for multiple positive solutions of a singular generalized Sturm-Liouville multipoint boundary value problem are established. The article ends with an illustrative example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of multiple positive symmetric solutions for fourth order p-Laplacian iterative system with integral boundary conditions. Initially, we establish the existence of at least one and two positive symmetric solutions for the fourth order problem using Krasnosel'skii fixed point theorem. Subsequently, we establish the existence of at least three positive symmetric solutions by applying fivefunctionals fixed point theorem. [ABSTRACT FROM AUTHOR]

A boundary value problem for a nonlinear second-order functional-differential equation on the interval with integral boundary conditions is considered. Sufficient conditions for the existence of at least one positive solution of the problem under consideration are found by using special topological tools. A nontrivial example in which the sufficient conditions for the unique solvability of the problem are satisfied is given. [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]

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]

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]

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]

We study the existence of positive solutions to the fourth-order two-point boundary value problem { u"" (t) + f (t, u(t)) = 0, 0 < t < 1, u' (0) = u' (1) = u"(0) = 0, u(0) = a[u], where α[u] = ∫0¹ u(t)dA(t) is a Riemann-Stieltjes integral with A ≥ 0 being a nondecreasing function of bounded variation and f ∈ C([0,1] x ℝ+, ℝ+). The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii's fixed point theorem and the Avery-Peterson fixed point theorem. [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]

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]

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solution of the following semipositone boundary value problem on time scales: \begin{align*} (\psi(t)y^\Delta (t))^\nabla + \lambda_1 g(t, \,y(t)) + \lambda_2 h(t,\,y(t)) = 0, \,t \in [\rho(c), \,\sigma(d)]_\mathbb{T}, \end{align*} with mixed boundary conditions \begin{align*} \alpha y(\rho(c))-\beta \psi(\rho(c)) y^\Delta(\rho(c))=0,\\ \gamma y(\sigma(d))+\delta \psi(d) y^\Delta(d)=0, \end{align*} where \(\psi:C[\rho(c),\, \sigma(d)]_\mathbb{T}\), \(\psi(t)>0\) for all \(t \in [\rho(c),\,\sigma(d)]_\mathbb{T}\); both \(g\) and \(h : [\rho(c),\,\sigma(d)]_\mathbb{T} \times [0,\,\infty) \to \mathbb{R}\) are continuous and semipositone. We have established the existence of at least one positive solution or multiple positive solutions of the above boundary value problem by using fixed point theorem on a cone in a Banach space, when \(g\) and \(h\) are both superlinear or sublinear or one is superlinear and the other is sublinear for \(\lambda_i>0;\,i=1,\,2\) are sufficiently small.

A model elliptic pseudodifferential equation in a polyhedral cone is considered, and the situation when some of the parameters of the cone tend to their limiting values is investigated. In Sobolev–Slobodetskii spaces, a solution of the equation in the cone is constructed in the case of a special wave factorization of the elliptic symbol. It is shown that a limit solution of the boundary value problem with an additional integral condition can exist only under additional constraints on the boundary function. [ABSTRACT FROM AUTHOR]

In this short note, we prove, by means of classical fixed point index, an affine version of a Birkhoff–Kellogg‐type theorem in cones. We apply our result to discuss the solvability of a class of boundary value problems for functional differential equations subject to functional boundary conditions. We illustrate our theoretical results in an example. [ABSTRACT FROM AUTHOR]

for stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space, the shock-front coincides with the upwind surface of the body, hence there is an infinite-thin layer of concentrated mass, in which all particles hitting the body move along its upwind surface. By proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations, which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces, the authors derive the compressible Euler equations for flows in concentration layers, which is a stationary pressureless compressible Euler system with source terms and independent variables on curved surface. As a by-product, they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows, which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics. [ABSTRACT FROM AUTHOR]

The existence of a positive solution to a system of nonlinear semipositone Hadamard fractional BVP with the p-Laplacian operator is examined in this research. The boundary value problem's associated Green's function and some of its properties are first obtained. Additionally, the existence results are established using the nonlinear alternative of the Leray–Schauder theorem and the Guo–Krasnosel'skii fixed-point theorem. [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]

We consider an elliptic pseudo-differential equation in a plane sector with additional integral condition. Using a formula for a general solution we study a limit case in which the size of a sector tends to zero. It is shown that the function in the boundary condition cannot be an arbitrary function, and it must satisfy some functional singular integral equation. [ABSTRACT FROM AUTHOR]

We study a class of boundary value problems (BVPs) for second order ordinary differential equations (ODEs). A new topological approach is developed and applied to prove the existence of at least two nonnegative classical solutions. The interesting points of our results are that derivative operator is time depending and the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. The arguments are based upon recent fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. An example is given to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

In this work a new functional expansion-compression fixed point theorem of Leggett-Williams type is developed for a class of mappings of the form T + F, where (I - T) is Lipschitz invertible map and F is a k -set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem. [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]

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this communication, thermodynamic irreversibility arising in dissipative Casson fluid flow inside a cone is investigated. The boundary–layer flow is considered wherein the motion is caused due to a point sink at the cone's vertex and the movement of the wall of the cone. The wall of the cone is subjected to mass transpiration that alters the flow and thermal regime. The cone having fluid‐saturated porous medium experiences Cattaneo–Christov heat flux. The configuration admits a similarity transformation that yields a boundary value problem (BVP) comprising an ordinary differential equation. The BVP is treated by the fourth‐order R‐K method along with the shooting algorithm. The system yields a dual solution for momentum and energy, which gives rise to a dual regime for entropy distribution. Numerical computations provide quantities of interest viz. velocity and temperature distributions, skin friction coefficient, Nusselt number, and entropy distribution. Phenomena exhibited through profiles/tables for velocity, temperature, entropy, streamlines, and other quantities of interest reveal interesting results. [ABSTRACT FROM AUTHOR]

In this work, we deal with the following two-point Dirichlet boundary value problem for a finite nabla fractional difference equation: ... Here a, b ∈ ℝ with b - a ∈ ℕ3, 1 < α < 2, f : ℝ → ℝ+ ∪ {0} is a continuous function, and ∇p(a)α denotes the αth- order Riemann-Liouville backward (nabla) difference operator. First, we establish an associated Greens function, and obtain some of its properties. Under suitable conditions on the non-linear part of the difference equation, we deduce some results on at least one and at least three positive solutions of the considered problem. For this purpose, we use a few prominent conical shell fixed-point theorems. [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]

In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones. [ABSTRACT FROM AUTHOR]

In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under the boundary conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound on the third-order derivative term, and the theory of fixed-point index is used on suitable open sets to obtain the existence of positive solutions. The nonlinearities have quadratic growth in the third-order derivative term. Previous results in the literature are not applicable in our case, as shown by our examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales TαΔ[ TβΔ (Vn(t))] = φ(t) fn(Vn+1(t)), t ∈ (0, 1)핋, 1 < α, β ≤ 2 V1(t) = Vl+1 (t), t ∈ (0, 1)핋, n = 1, 2, ..., l, satisfying two-point Riemann--Stieltjes integral boundary conditions Vn(0) = 0, Vn(1) = ∫0¹ Vn(τ)g(τ), n = 1, 2, ..., l, (TβΔVn)(0) = 0, (TβΔVn) (1) = ∫0¹ (TβΔVn) (τ)g(τ), n = 1, 2, ..., l, where T*Δ denotes the conformable fractional derivative of order * ∈ {α, β} on time scale T, by an application of Krasnoselskii's fixed point theorem on a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nabla fractional order boundary value problem ... where j = 1, 2, . . . ,N, zN+1 = z1, N ∈ N, n0, n ∈ R with n - n0 ∈ N and derive sufficient conditions for the existence of positive solutions by an application of Krasnoselskii's fixed point theorem on a Banach space. Later, we derive sufficient conditions for the existence of a unique solution by applying Rus's contraction mapping theorem in a metric space, where two metrics are employed. [ABSTRACT FROM AUTHOR]

The authors study the existence of positive solutions of singular Sturm-Liouville boundary value problem... [ABSTRACT FROM AUTHOR]

In this paper, we consider Riemann-Liouville two-point fractional order boundary value problem having denumerably many singularities and determined sufficient conditions for the existence of denumerably many positive solutions by an application of Krasnoselskii's cone fixed point theorem in a Banach space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters: { u (4) (t) + β 1 u ″ (t) − α 1 u (t) = f 1 (t , u (t) , v (t)) , 0 < t < 1 ; v (4) (t) + β 2 v ″ (t) − α 2 v (t) = f 2 (t , u (t) , v (t)) , 0 < t < 1 ; u (0) = u (1) = u ″ (0) = u ″ (1) = 0 ; v (0) = v (1) = v ″ (0) = v ″ (1) = 0 , where f 1 , f 2 ∈ C [ (0 , 1) × R 0 + × R , R ] , R 0 + = (0 , + ∞) . By constructing a special cone and applying fixed point index theory, some new existence results of multiple solutions for the considered system are obtained under some suitable assumptions. Finally, an example is worked out to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider nonlinear second order m-point impul- sive time scale boundary value problems on infinite intervals. We establish criteria for the existence of positive solutions to the nonlinear impulsive time scale boundary value problems on infinite intervals by using a result from the theory of fixed point index. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder's fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a higher order p-Laplacian differential equations, By applying Five functional fixed point theorem, we establish sufficient conditions for the existence of triple positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the higher-order multi-point fractional boundary value problem. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point fractional boundary value problem by using the Krasnosel'skii fixed point theorem and the Legget-Williams fixed point theorem, respectively. [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 the paper we consider the boundary value problem of heat conduction outside the cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary condition contain a derivative with respect to the time variable. The peculiarity of the problem under consideration consists precisely in the presence of a moving boundary and the degeneration of the solution domain into a point at the initial moment of time. The well-known classical methods are generally not applicable to this type of problems. By the method of heat potentials, such boundary value problems of heat conduction are reduced to the solution of singular Volterra type integral equations of the second kind A singular Volterra type equation is understood as an equation whose kernel has the following property: the integral of the kernel of the equation does not tend to zero as the upper limit tends to the lower one. Such integral equations cannot be solved by the method of successive approximations, and in most cases the corresponding homogeneous integral equations have nonzero solutions. We prove a theorem on the solvability of the considered boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We found a nonzero solution of this singular integral equation. [ABSTRACT FROM AUTHOR]

The wave equation ∂ t t − c 2 Δ x u (x , t) = e − t f (x , t) in the cone { (x , t) : ∥ x ∥ ≤ t , x ∈ R d , t ∈ R + } is shown to have a unique solution if u and its partial derivatives in x are in L 2 (e − t) on the cone, and the solution can be explicit given in the Fourier series of orthogonal polynomials on the cone. This provides a particular solution for the boundary value problems of the non-homogeneous wave equation on the cone, which can be combined with a solution to the homogeneous wave equation in the cone to obtain the full solution. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order ODE with multi-point boundary conditions and an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on cones. [ABSTRACT FROM AUTHOR]

Motivated by the study of systems of higher-order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral equations, where the nonlinearities and the functionals involved depend on some derivatives. We improve and complement earlier results in the literature. We also provide some examples in order to illustrate the applicability of the theoretical results. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'. [ABSTRACT FROM AUTHOR]

In this paper, we study system of even order two-point singular boundary value problems with integral boundary conditions on time scales and establish the existence of denumerably many symmetric positive solutions. The proofs of our main results are based on the Holder's inequality and Krasnoselskii's fixed point theorem. [ABSTRACT FROM AUTHOR]

We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the following nonlinear differential equation -u"(t) + k²u(t) = f(t, u(t)); t ∊ [0; 1] with three point boundary conditions, u(0) = 0; u(1) = αu(n) where k > 0; 0 < n < 1, α ∊ R f: [0, 1] × R+ ≚ R+: By means of Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem, the authors establish existence of two and three positive solutions. Examples are also given to illustrate the main results. [ABSTRACT FROM AUTHOR]

The sufficient conditions are derived for the existence of denumerably many positive solutions for fractional order boundary value problem... whereDε0+, Dη0+ denote fractional derivatives of Riemann-Liouville type with 0 < ε < 1,2 < η ≤3, Iδ0+ (δ ∈ R)denotes Riemann-Liouvillefractional integral, φ: R → Ris an increasing homeomorphism and positive homomorphism operator (IHPHO), by applying Hölder's inequalityand Krasnoselskii's cone fixed point theorem in a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the positive solutions of beam equations with the nonlinearities including the slope and bending moment under nonlocal boundary conditions involving Stieltjes integrals. We pose some inequality conditions on nonlinearities and the spectral radius conditions on associated linear operators. These conditions mean that the nonlinearities have superlinear or sublinear growth. The existence of positive solutions is obtained by fixed point index on cones in C 2 [ 0 , 1 ] , and some examples are given for beam equations subject to mixed integral and multi-point boundary conditions with sign-changing coefficients. [ABSTRACT FROM AUTHOR]