Existence and Multiplicity of Nontrivial Weak Solutions for Kirchhoff-type Fractional $p$-Laplacian Equation

TL;DR

This paper investigates the existence and multiplicity of nontrivial weak solutions for a Kirchhoff-type fractional p-Laplacian Dirichlet problem using critical point theory, specifically mountain pass theorem and genus properties.

Contribution

It introduces new results on solutions for a fractional p-Laplacian problem with Kirchhoff-type nonlinearity, employing advanced variational methods.

Findings

Established existence of weak solutions

Proved multiplicity of solutions under certain conditions

Applied mountain pass theorem and genus theory

Abstract

We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the mountain pass theorem and the genus properties in critical point theory, we get some new results on the existence and multiplicity of nontrivial weak solutions for such Dirichlet problem.