On sequences of homoclinic solutions for fractional discrete p-Laplacian equations

Abstract

In this paper, we consider the following discrete fractional $ p $-Laplacian equations: $ \begin{equation*} (-\Delta_{1})^{s}_{p}u(a)+V(a)|u(a)|^{p-2}u(a) = \lambda f(a, u(a)), \; \mbox{in}\ \mathbb{Z}, \end{equation*} $ where $ \lambda $ is the parameter and $ f(a, u(a)) $ satisfies no symmetry assumption. As a result, a specific positive parameter interval is determined by some requirements for the nonlinear term near zero, and then infinitely many homoclinic solutions are obtained by using a special version of Ricceri's variational principle.

Keywords

• discrete fractional $ p $-laplacian
• homoclinic solutions
• ricceri's variational principle