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In this paper, we concern with a 2nth-order discrete system. Using the critical point theory, we establish various sets of sufficient conditions for the existence of periodic solutions with prescribed minimal period. To the best of our knowledge, this is the first time to discuss the periodic solutions with prescribed minimal period for a 2nth-order discrete system.

The authors explore the boundary value problems of a discrete generalized beam equation. Using the critical point theory, some sufficient conditions for the existence of the solutions are obtained. Several consequences of the main results are also presented. Examples are given to illustrate the theorems.

In this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T+ 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

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.

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.

By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

By using the critical point theory, the existence of a nontrivial homoclinic orbit which decays exponentially at infinity for difference equations containing both advance and retardation is obtained. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results obtained successfully extend and complement the results in the literature.

In this paper, a class of fourth-order nonlinear difference equations are considered. By making use of the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problems and give some new results. Our results successfully complement the existing ones.

Using the critical point theory, the existence of periodic solutions for a 2 $$n$$ th-order nonlinear difference equation containing both advance and retardation involving $$p$$ -Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2 $$n$$ th-order $$p$$ -Laplacian difference equation. The obtained results successfully generalize and complement the existing ones.

In this paper, a fourth-order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence and nonexistence of solutions for Neumann boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

In this paper, a fourth-order nonlinear difference equation is considered. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for mixed boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for mixed boundary value problem and give some new results. Recent results in the literature are generalized and significantly complemented.

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 Dirichlet boundary value problems and give some new results. Our results successfully complement the existing ones. Copyright (c) 2014 John Wiley & Sons, Ltd.

By using the critical point method, some new criteria are obtained for the existence and multiplicity of periodic solutions for fourth-order nonlinear functional difference equations. The proof is based on the linking theorem in combination with variational technique. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.

In this article, we establish the existence of at least three unbounded posi- tive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic and subharmonic solutions to a 2 n th-order nonlinear difference equation containing both advance and retardation involving p -Laplacian. The proof is based on the Linking Theorem in combination with variational technique. Our results generalize and improve the results in the literature.

By using the critical point theory, the existence of periodic solutions for 2$n$th-order nonlinear $p$-Laplacian difference equations is obtained. The main approaches used in our paper are variational techniques and the Saddle Point theorem. The problem is to solve the existence of periodic solutions for 2$n$th-order $p$-Laplacian difference equations. The results obtained successfully generalize and complement the existing ones.

By using the critical point theory, the existence of periodic solutions for a $2n$th-order nonlinear difference equation is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a $2n$th-order nonlinear difference equation. Results obtained successfully complement the existing one.

By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic solutions to a class of nonlinear difference equations. The proof is based on the Linking Theorem in combination with variational technique. Our results successfully generalize and improve some existing results in the literature.

In this paper, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to second order p-Laplacian difference equations are obtained by using the critical point theory. The proof is based on the Linking theorem in combination with variational technique.

This paper is concerned with a class of fourth-order nonlinear difference equations. By making use of the critical point theory, we establish various sets of sufficient conditions for the nonex- istence and existence of solutions for mixed boundary value problem and give some new results. Results obtained generalize and comple- ment the existing ones.