Multiple Solutions for the Nonhomogeneous Schrödinger-Poisson Equations Involving the Fractional Laplacian

Abstract

In this work, we consider the Schrodinger-Poisson equations with the fractional Laplacian of order α in R^n. Under some suitable assumptions on potential V(x) and the nonlinear term f(x, u), the existence of multiple solutions is proved by using the Mountain Pass Theorem and the Ekeland's variational principle in critical point theory. As a special case, we prove the existence of two nontrivial radial solutions when V(x)=1, f(x, u)=|u|^p-2 u.