Multiple solutions for a class of oscillatory discrete problems

Abstract

In this paper, we study a discrete nonlinear boundary value problem that involves a nonlinear term oscillating at infinity and a power-type nonlinearity up. By using variational methods, we establish the existence of a sequence of non-negative weak solutions that converges to +∞ if 0 < p ≤ 1. In the superlinear case, we establish a sufficient condition for the existence of at least n solutions.

Keywords

• difference equations
• discrete laplacian
• oscillatory nonlinearities
• variational methods
• 39a14
• 47j30