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

TL;DR

This paper proves the existence of infinitely many weak solutions for a fractional p-Laplacian equation with sign-changing potential using a variant of the fountain Theorem, expanding solution multiplicity results in nonlinear fractional PDEs.

Contribution

It introduces a novel application of the fountain Theorem to fractional p-Laplacian equations with sign-changing potentials, demonstrating multiple solutions.

Findings

Existence of infinitely many weak solutions established.

Applicable to equations with sign-changing potentials.

Utilizes a variant of the fountain Theorem for proof.

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 (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where $s \in (0,1)$,$ p \geq 2$,$ N \geq 2$, $(-\Delta)^{s}_{p}$ 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.