On sequences of large homoclinic solutions for a difference equations on the integers involving oscillatory nonlinearities

Abstract

In this paper, we determine a concrete interval of positive parameters $\lambda$, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem $-\Delta \left(a(k){\varphi }_p(\Delta u(k-1))\right)+b(k){\varphi }_p(u(k))=\lambda f(k,u(k))$, $k\in Z$; where the nonlinear term $f:Z\times R\to R$ has an appropriate oscillatory behavior at infinity, without any symmetry assumptions. The approach is based on critical point theory.

Cited by in corpus (1)

• On homoclinic solutions for a second order difference equation with p-Laplacian