Yuanbiao Zhang

Existence theorems of periodic solutions for second-order difference equations containing both advance and retardation

Using the critical point method, the existence of periodic solutions for second-order nonlinear difference equations containing both advance and retardation is established. The proof is based on the Saddle Point Theorem in combination with variational technique.

Periodic and subharmonic solutions for fourth-order nonlinear difference equations☆

Abstract By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic and subharmonic solutions to fourth-order nonlinear difference equations. The main approach used in our paper is a variational technique and the Linking Theorem. Our results generalize and improve the existing ones.

Boundary value problems of second order nonlinear difference equations with Jacobi operators

The paper is devoted to a question of existence and multiplicity of solutions of boundary value problems for a class of second order nonlinear difference equations with Jacobi operators. By using the critical point theory, some sufficient conditions are obtained.

On the nonexistence and existence of solutions for a fourth-order discrete Dirichlet boundary value problem

Abstract This paper is concerned with a class of fourth-order nonlinear difference equations. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for a Dirichlet boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

Existence and nonexistence results for a 2n-th order p-Laplacian discrete Dirichlet boundary value problem

In this paper 2n-th order p-Laplacian difference equations are considered. Using the critical point method, we establish various sufficient conditions for the existence and nonexistence of solutions for Dirichlet boundary value problem. Recent results in the literature are generalized and significantly complemented, as well as, some new results are obtained.

Periodic and subharmonic solutions for 2nth-order p-Laplacian difference equations

By using the critical point theory, some new criteria for the existence and multiplicity of periodic and subharmonic solutions for 2nth-order p-Laplacian difference equations are obtained. The proof is based on the Linking Theorem in combination with variational technique. Our results generalize and improve the known in the literature results.