Search

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 article, some new existence criteria of at least one solution to boundary value problems for a fourth-order difference equation are obtained by using the critical point theory. In a special case, a necessary and sufficient condition for the existence and uniqueness of solution is also established. An example of the main result is given.

In this article, we study a discrete fourth order boundary value problem. By making use of variational methods and critical point theory, we obtain some criteria for the existence and multiple solutions. Moreover, two examples are included to illustrate the applicability of the main results.

This paper is devoted to investigate a question of the existence of solutions to boundary value problems for a class of nonlinear difference systems. The proof is based on the notable mountain pass lemma in combination with variational technique. By using the critical point theory, some new existence criteria are obtained.

This paper is concerned with boundary value problems for a fourth-order nonlinear difference equation. Via variational methods and critical point theory, sufficient conditions are obtained for the existence of at least two nontrivial solutions, the existence ofndistinct pairs of nontrivial solutions, and nonexistence of solutions. Some examples are provided to show the effectiveness of the main results.

In this paper, we investigate the solutions of boundary value problems for second-order p-Laplacian difference equations. By using the critical point theory, the existence and multiple results are obtained.

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.

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.

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 employing a critical point theorem, established by Bonanno, we prove the existence of three distinct solutions to boundary value problems of nonlinear difference equations with a discretep-Laplacian operator. To demonstrate the applicability of our results, we also present an example.

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.

We establish the results on the existence of three positive solutions to Sturm-Liouville boundary value problems of the singular fractional differential equation with the nonlinearity depending on D μ 0+ u ⎧ ⎪ ⎪ D α+u(t)+f(t,u(t),D μ+ u(t)) = 0, t ∈ (0,1),1 < α < 2

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, some sufficient conditions for the existence and multiplicity of the boundary value problems to a class of second order functional difference equations are obtained.

In this paper, some sufficient conditions for the existence and multiplicity of the boundary value problems to a class of second order functional difference equations are obtained by using the critical point theory.

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 using critical point theory, Lyapunov-Schmidt reduction method, and characterization of the Brouwer degree of critical points, sufficient conditions to guarantee the existence of five or six solutions together with their sign properties to discrete second-order two-point boundary value problem are obtained. An example is also given to demonstrate our main result.