Ilkay Yaslan Karaca

Higher-order three-point boundary value problem on time scales

In this paper, we consider a higher-order three-point boundary value problem on time scales. We study the existence of solutions of a non-eigenvalue problem and of at least one positive solution of an eigenvalue problem. Later we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.

Fourth-order four-point boundary value problem on time scales

Abstract In this work, we consider a fourth-order four-point boundary value problem for dynamic equations on time scales. We establish criteria for the existence of a solution and a positive solution by using the Leray–Schauder fixed point theorem. We also give an example to illustrate our results.

Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales

In this paper, we make use of the four functionals fixed point theorem to verify the existence of at least one symmetric positive solution of a second-order m-point boundary value problem on time scales such that the considered equation admits a nonlinear term f whose sign is allowed to change. The discussed problem involves both an increasing homeomorphism and homomorphism, which generalizes the p-Laplacian operator. An example which supports our theoretical results is also indicated.MSC:34B10, 39A10.

Positive Solutions of nth-Order Boundary Value Problems with Integral Boundary Conditions

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

Existence of positive solutions for third-order boundary value problems with integral boundary conditions on time scales

In this paper, four functionals fixed point theorem is used to verify the existence of at least one positive solution for third-order boundary value problems with integral boundary conditions for an increasing homeomorphism and homomorphism on time scales. We also provide an example to demonstrate our results.MSC:34B18, 34N05.

Positive Solutions for Boundary Value Problems of Second-Order Functional Dynamic Equations on Time Scales

Criteria are established for existence of least one or three positive solutions for boundary value problems of second-order functional dynamic equations on time scales. By this purpose, we use a fixed-point index theorem in cones and Leggett-Williams fixed-point theorem.

Positive solutions of nth-order m-point impulsive boundary value problems

Abstract This paper is concerned with the existence of positive solutions of an nth-order m-point impulsive boundary value problem. Existence results of at least three positive solutions are established via a fixed point theorem in a cone due to Avery–Peterson. Also, an example is given to illustrate the effectiveness of our result.

On positive solutions for second-order boundary value problems of functional differential equations

In this paper, by using Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions of a second-order boundary value problem for a class of nonlinear functional differential equations. Examples are also included to illustrate our results.

Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.

Instability intervals of a hill's equation with piecewise constant and alternating coefficient

Abstract In this paper, we obtain asymptotic formulas for eigenvalues of the periodic and the semiperiodic boundary value problems associated with a Hills equation having piecewise constant and alternating coefficient. As a corollary, it is shown that the lengths of instability intervals of the considered Hills equation tend to infinity.