Search

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.

We investigate the discrete nonlinear Schrodinger equations with indefinite sign subquadratic potentials. Making use of the critical point theory, we obtain a new result concerning the existence of a standing wave solution.

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.

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.

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.

In this paper, we obtain a new sufficient condition on the existence of breathers for the discrete nonlinear Schrodinger equations by using critical point theory in combination with periodic approximations. The classical Ambrosetti–Rabinowitz superlinear condition is improved.

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 of the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. The existing results are generalized and significantly complemented.

Using the critical point theory, we obtain the existence of a nontrivial homoclinic orbit for second order \(p\)-Laplacian difference equations containing both advance and retardation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. One of our results generalizes and improves the results in the literature.

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.

By making use of the critical point theory, the existence of periodic solutions for a class of nonlinear difference equations is obtained. The proof is based on the saddle point theorem in combination with variational technique. The problem is to solve the existence of periodic solutions of a class of nonlinear difference equations. Results obtained complement the existing one.

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.

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.

In this paper, a 2\(n\)th-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. Recent results in the literature are generalized and significantly complemented.

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.

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.

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.

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.

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.

In this paper, a second order p-Laplacian difference equation is considered. By using the critical point theory, we obtain the existence of a nontrivial homoclinic orbit and give some new results. The proof is based on the Mountain Pass Lemma in combination with periodic approximations.

By using of the critical point method, the existence of periodic solutions for fourth-order nonlinear functional 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 of fourth-order nonlinear functional difference equations. Results obtained generalize and complement the existing one.

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.

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.Keywords: Nonexistence and existence, Dirichlet boundary value problem, fourth-order, mountain pass lemma, discrete variational theory.

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.

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.

By using the critical point theory, the existence of periodic solutions to second order nonlinear p-Laplacian difference equations is obtained. The main approach used is a variational technique and the saddle point theorem. The problem is to solve the existence of periodic solutions of second order nonlinear p-Laplacian difference equations.

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.

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.

In this paper, a fourth-order nonlinear difference equation is considered.By making use of the critical point theory, we establish various sets ofsufficient conditions for the existence and nonexistence of solutions forDirichlet boundary value problem and give some new results. Ourresults generalize and complement the results in the literature.&nbsp

By making use of the critical point theory, the existence of periodic solutions for fourth-order nonlinear difference equations is obtained. The proof is based on the Saddle Point Theorem in combination with variational technique. The problem is to solve the existence of periodic solutions of fourth-order nonlinear difference equations. Results obtained complement the existing one.