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In this paper, we establish some new existence results for certain coupled systems of nonlinear Ψ-fractional differential equations with four-point fractional integral boundary conditions. The proofs are derived from Banach fixed point theorem. As an application, a nontrivial example is presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we study a class of p(x)-Kirchhoff type problem with Steklov boundary value in variable exponent Sobolev spaces. Precisely, we show the existence of at least three solutions and a nontrivial weak solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections. [ABSTRACT FROM AUTHOR]

Goal Programming (GP), as a generalization of linear programming, is a proper technique for handling Multi-Objective Decision-Making (MODM) problems. Using this technique, we can determine multiple aspiration levels for each objective. The Neutrosophic Set (NS) theory is a powerful tool to deal with indeterminacy and inconsistent data. This paper provides a new idea to formulate Neutrosophic Multi-Choice Goal Programming (NMCGP) problems to simulate real-life situations more realistically. Also, to show the low computational complexity of the proposed model, the Space and Time complexity criteria are used in the Python language. Eventually, a practical mathematical example is solved to present the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (−∆)mu − ∆ut = uk−2u ln |u| . We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound of blow-up time is considered. This improves and extends some previous studies. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, by using invariants of Riemann and general solutions of Euler–Poisson– Darboux–Riemann equations, a new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics is given. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear Liouville–Caputo fractional differential equations equipped with a new set of nonlocal boundary conditions involving an arbitrary strip together with two sets of nonlocal multi-points on either part of the strip on the given domain. We emphasize that the boundary conditions considered in this study are formulated with respect to the sum and difference of the unknown functions. We apply the well-known tools of the fixed point theory to derive the main results. Examples are presented for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method and contraction mappings principle, the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the considered inverse coefficient problem is proved for the smaller value of time. [ABSTRACT FROM AUTHOR]

In this paper, we give some characterizations on S-curvature in Randers measure spaces, which shows that only the Busemann-Hausdorff volume form can admit a vanishing S-curvature. [ABSTRACT FROM AUTHOR]

n the paper we consider canonical almost geodesic mappings π2(e), e = ±1, of spaces with affine connection onto 2-symmetric, 3-symmetric and m-symmetric spaces. The main equations for the mappings have been obtained as closed systems of PDEs of Cauchy type in covariant derivatives. We have found the maximum numbers of essential parameters which the general solutions of the systems depend on. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Hermite-Hadamard type inequalities for uniformly convex functions with respect to geodesic in Hadamard space. Also, we give some application of these functions in means. [ABSTRACT FROM AUTHOR]

In the present paper, we proposed a new sequence of summation-integral type operators involving Apostol-Genocchi polynomials. We study some approximation results of the proposed operators using first and second-order modulus of continuity, the global rate of convergence using Voronovskaja-type asymptotic theorem, Lipschitz-type space, and Ditzian-Totik modulus of smoothness. Lastly, we study the weighted approximation. [ABSTRACT FROM AUTHOR]

In this paper, new weighted Hermite-Hadamard type inequalities for differentiable preinvex and prequasiinvex functions are proved. These results generalize many results proved in earlier works for these classes of functions. [ABSTRACT FROM AUTHOR]

In this paper, a new class of multi-agent systems with addictive and multiplicative measurement noises under Markovian switching topologies is introduced. Some sufficient conditions of average consensus to the systems are also established under consideration. First, based on the continuous-time Markov chain with finite modes, the time-varying topologies of the considering system is figured. Then, the mean square average consensus for the multi-agent systems with a time-varying gain under the time-varying topologies and the Markov chain is studied. Finally, the example and simulation results are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results. [ABSTRACT FROM AUTHOR]

This paper deals with the initial boundary value problem for a higher-order parabolic equation with logarithmic source term ... . By employing the potential wells technique we show the global existence of the weak solution. Also, we obtain the exponential decay for the weak solutions. [ABSTRACT FROM AUTHOR]

In this paper, all normal extensions of the minimal operator associated with the singular degenerate linear differential expressions for first order in the Hilbert space of vector-functions are investigated in terms of boundary values. As well, it analyses the spectrum parts of any normal extension. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of positive solutions for the semipositone fractional boundary value problem with n point fractional integral boundary conditions. The existence of positive solutions is established using the five functionals fixed point theorem. An example is given to ratify that our main result is theoretically feasible. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of a non-trivial solution in W 1,p(x) 0 (Ω) for the problem ( ∆p(x)u = f(x,u,∇u) in Ω, u = 0 in Ω. The proof is based on Schaefer's fixed point theorem. [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, the initial-value problem for a linear second order delay differential equation is considered. To solve this problem numerically, an appropriate difference scheme is constructed by using the method of integral identities which contains basis functions and interpolating quadrature rules with weight and remainder term in integral form. Besides, the method is proved to be first-order convergent in discrete maximum norm. The numerical illustration provided support the theoretical results. Finally, the proposed method is compared with the implicit Euler method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a model of linear thermoelasticity for an elastic threedimensional body with high thermal conductivity covered by a thin layer on one of its faces. We show that Ventcel's boundary conditions may be obtained, as the thickness of the rigid body goes to zero. [ABSTRACT FROM AUTHOR]

This paper concerns the investigation of controllability and Hyers-Ulam stability of initial value problems for fractional differential equations via generalized proportional-Caputo fractional derivatives. The main results are obtained by means of the Krasnoselskii's fixed point theorem. [ABSTRACT FROM AUTHOR]

The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic. [ABSTRACT FROM AUTHOR]

The paper is concerned with the existence of positive weak solutions for a new class of (p;q)-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign conditions for γ(0),g(0), f(0) and h(0). Moreover, a multiplicity result is obtained when γ(0) = g(0) = f(0) = h(0) = 0: Finally, we give some examples to verify our main results. [ABSTRACT FROM AUTHOR]

In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuity coefficient is considered. The half inverse problems is studied of determining the coefficient and two potential functions of the boundary value problem its spectrum by Hocstadt-Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from the spectrum. [ABSTRACT FROM AUTHOR]

The problem of identifying of the several unknown time dependent parameters in the minor coefficient and in the special type right-hand side function of the semilinear higher order ultraparabolic equation from the additional initial, boundary and integral type overdetermination conditions is considered in this paper. The sufficient conditions of the unique solvability on the interval [0;T]; where T is determined by the coefficients of the equation, are obtained. [ABSTRACT FROM AUTHOR]

The paper gives multiplicity results for the impulsive boundary value problem x" = f(t,x), for a.e. t ∈ [0,T], such that x(t) ∈ int K, x'(s +) = -x'(s-), if s ∈ (0,T), x(s) ∈ ∂K, x(0) = A, x(T) = B, where K ⊂ R is a compact interal, f is Carathéodory function on [0,T]?× K and A, B ∈ int K. This problem can be understood as a problem in one-dimensional billiard space and it is also a generalization of oscillator with obstacles from below and from above and absolutely elastic impacts. A simple condition for the existence of solution with exact number of impacts is given, as well as the multiplicity result. The results are obtained by a transformation into problem without impulses (without impacts) and using Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper we study some properties of the solutions of a second order system of functional-differential equations with maxima, of mixed type, with "boundary" conditions. We use the weakly Picard operator technique. [ABSTRACT FROM AUTHOR]

In this paper, the approximate solutions by using the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear boundary value problems with constant coefficients are investigated. Thus, comparisons of the found solutions are given. [ABSTRACT FROM AUTHOR]

In this paper,we study the existence and multiplicity of solutions for a perturbed three-point boundary value problem of Kirchhoff-type. The approach is based on variational methods and critical point theory.As applications of these methods,we get several multiplicity results for the problems under consideration. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with 2p-order Hamiltonian systems with impulsive effects. We investigate the variational structure associated to this system. In addition, we obtain some results of multiple solutions for asymptotically linear 2p-order Hamiltonian systems via variational methods and critical point theorems. Meanwhile, some examples are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

We consider the following second order impulsive differential equation with delays ... In this paper we obtain sufficient conditions of nonpositivity of Green's functions for impulsive differential equation. All results are formulated in the form of theorems about differential inequalities. It should be noted that the sign-constancy of the coefficients bj (t) was assumed in all the literature devoted to impulsive functional differential equations. One of the main purposes of this work is to propose a technique allowing us to avoid these assumptions. [ABSTRACT FROM AUTHOR]

This study is concerned with a singularly perturbed three-point boundary-value problem with delay. Firstly, bounds on the solution and its derivative of the solution to be used later in the paper are obtained. To solve it numerically, we use an exponentially fitted difference scheme on an equidistant mesh which is established by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. Then, the stability and convergence analysis of difference scheme is given and it is uniformly convergent in perturbation parameter. Furthermore, numerical results which show the effectiveness of the method are presented. [ABSTRACT FROM AUTHOR]

This paper deals with the Sturm-Liouville equation with a finite number of point δ-interactions and eigenvalue parameter contained in the boundary condition. Sturm-Liouville problem with discontinuities at one or two points and its different variants have already been investigated. In this study we extend these results to a finite number of point δ-interactions case. The crucial part of this study is the using graph demonstration to obtain asymptotic representation of solutions. [ABSTRACT FROM AUTHOR]

Zeros of minimizers of p-Ginzburg-Landau functional are helpful to understand the location of vortices of superconductivity and superfluid. When p D 2 and the degree of the boundary data around the boundary is ±1, there exists only one zero of the p-Ginzburg-Landau minimizers in the bounded domain. When p > 2, this becomes a more complicated problem. This paper is concerned with the location of the zeros of a radial minimizer of a p-Ginzburg-Landau type functional. The authors use the method of moving planes and the idea of the proof of Pohozaev's identity to verify that the origin is the unique zero of the radial minimizer in the domain. [ABSTRACT FROM AUTHOR]

In this paper we consider the following nonlocal boundary value problems (p(t)x')'=f(t,x,x'), x'(0)=∣0, x(1)=∫10 x'(s)dg(s) and (p(t)x')'=f(t,x,x'), x'(0)=0, x(1)=∫10 x(s)dg(s), where f:[0,1]×Rk×Rk → Rk and the integrals are meant in the sense of Riemann-Stieltjes. Under a sign condition on the function f , we prove the existence of solutions [ABSTRACT FROM AUTHOR]

Let R be a *-prime ring with characteristic different from two and U ≠ 0 be a square closed *-Lie ideal of R. An additive mapping F : R → R is called an generalized derivation if there exits a derivation d : R → R such that F(xy) = F(x)y+xd(y). In the present paper, it is shown that U ⊆ Z if R is a *-prime ring which admits a generalized derivation satisfying several conditions that are associated with a derivation commuting with *. [ABSTRACT FROM AUTHOR]

In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin occurs at the first claim. It assures that the integral equation satisfied by the Gerber- Shiu function has a unique bounded solution and it is exactly the Gerber-Shiu function. By the help of the proven necessary and sufficient condition we can also simplify the theorem concerning the necessary and sufficient condition for the limit property. We do not assume independence between the inter-claim time and the claim size but the results can be applied to the usually investigated independent case as well. We present examples to show the applicability of the condition. [ABSTRACT FROM AUTHOR]

In this paper, we extend some spectral properties of regular Sturm-Liouville problems to those which consist of a Sturm-Liouville equation with discontinuous weight at two interior points together with spectral parameter-dependent boundary conditions. By modifying some techniques of [C. T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977) 293-308; O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694], we give an operator-theoretic formulation for the considered problem and obtain asymptotic formulas for the eigenvalues and eigenfunctions. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for boundary value problems of fractional differential equations of order q ∊ (0, 1] with four-point integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the quasilinearization for Riemann-Liouville fractional differential equations with two point boundary condition. By establishing a new comparison principle we get a monotone sequence which converges quadratically to the unique solution of the fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we present some existence, uniqueness and Hyers-Ulam stability results for the coupled fixed point of a pair of contractive type operators on complete metric spaces. The approach is based on a Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given. [ABSTRACT FROM AUTHOR]

The paper treats a linear overdetermined system which contains second order hyperbolic equations with two linear super singularities. The authors obtain some new integral representations of the solutions. [ABSTRACT FROM AUTHOR]

This paper concerns the study of the quenching time of the solution of the initialboundary value problem for a system of reaction-diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper we prove existence results for boundary value problems for higher-order differential inclusion x(n) (t) ϵ F(t, x (t)) with nonlocal boundary conditions, where F is a compact convex L¹-Carathéodory multifunction. [ABSTRACT FROM AUTHOR]