Infinitely many solutions for a nonlinear difference equation with oscillatory nonlinearity

Abstract

In this paper, we study a discrete nonlinear boundary value problem that involves a nonlinear term oscillating near the origin and a power-type nonlinearity $$u^p$$ . By using variational methods, we establish the existence of a sequence of non-negative weak solutions that converges to 0 if $$p\ge 1$$ . In the sublinear case, we prove that for all n positive integer, the problem has at least n weak solutions if the parameter lies in a certain range.