Infinitely Many Weak Solutions for Fractional Dirichlet Problem with $p$-Laplacian

TL;DR

This paper proves the existence of infinitely many weak solutions for a fractional p-Laplacian Dirichlet problem using critical point theory and genus properties.

Contribution

It introduces new criteria leveraging genus properties to establish infinitely many solutions for fractional p-Laplacian problems.

Findings

Established criteria for existence of infinitely many solutions

Applied critical point theory to fractional derivatives

Extended solution existence results to fractional p-Laplacian

Abstract

We focus on the study of $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the genus properties in critical point theory, we establish some new criteria to guarantee the existence of infinitely many weak solutions for the considered problem.