A discrete boundary value problem

A Note on a Fourth Order Discrete Boundary Value Problem

Using variational methods we investigate the existence of solutions and their dependence on parameters for certain fourth order difference equations.

Positive Solutions to a Second-Order Discrete Boundary Value Problem

A Discrete Boundary Value Problem in Banach Spaces

In this paper we present existence theorems for the second order discrete boundary value problem in Banach spaces under weaker conditions we have known. We suppose the weak sequential continuity and some conditions expressed in terms of the measure of weak noncompactness.

Three Positive Solutions to a Discrete Focal Boundary Value Problem

We are concerned with the discrete focal boundary value problem ∆3x(t−k) = f(x(t)), x(a) = ∆x(t2) = ∆2x(b+ 1) = 0. Under various assumptions on f and the integers a, t2, and b we prove the existence of three positive solutions of this boundary value problem. To prove our results we use fixed point theorems concerning cones in a Banach space.

Nonexistence and existence results for a 2$n$th-order $p$-Laplacian discrete Neumann boundary value problem

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.