Multiple solutions for a fractional $p$-Laplacian equation with sign-changing potential

Abstract

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-Δ)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where $s\in (0,1)$,$p\ge 2$,$N\ge 2$, $(-\Delta {)}_p^s$ is the fractional $p$-Laplace operator, the nonlinearity f is $p$-superlinear at infinity and the potential V(x) is allowed to be sign-changing.

References in corpus (2)

• Fractional p-eigenvalues
• Existence and symmetry result for Fractional p-Laplacian in ${\mathbb{R}}^n$

Cited by in corpus (6)

• Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional $p$-Laplacian
• Ground state solutions for a fractional Schrödinger equation with critical growth
• Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in ${\mathbb{R}}^N$
• Existence, multiplicity and concentration for a class of fractional $p\&q$ Laplacian problems in ${\mathbb{R}}^N$
• Infinitely many solutions for a class of fractional Orlicz-Sobolev Schrödinger equations
• On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in ${\mathbb{R}}^N$