Xia Liu

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.

Periodic and subharmonic solutions for a 2nth-order nonlinear difference equation

By using the critical point method, some new criteria are obtained for the existence and multiplicity of periodic and subharmonic solutions to a 2nth-order nonlinear dierence equation. The proof is based on the Linking Theorem in combination with variational technique. Our results generalize and improve some known ones. 2000 AMS Classification: 39A11.

Homoclinic orbits for second order nonlinear p-Laplacian difference equations

The paper proves the existence of nontrivial homoclinic orbits for second order nonlinear p-Laplacian difference equations without assumptions on periodicity using the critical point theory. Moreover, if the nonlinearity is an odd function, the existence of an unbounded sequence of nontrivial homoclinic orbits is proved.

Homoclinic orbits of 2nth-order difference equations involving p-Laplacian*

By making use of the critical point theory, we establish some new existence criteria to guarantee that a 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian has a nontrivial homoclinic orbit. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.

Existence of periodic solutions of fourth-order p-Laplacian difference equations*

By making use of the critical point theory, the existence of periodic solutions for fourth-order nonlinear p-Laplacian difference equations is obtained. The main approach used in our paper is a variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions of fourth-order nonlinear p-Laplacian difference equations. The results obtained successfully generalize and complement the existing one.

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.