Ground State Solutions of Kirchhoff-type Fractional Dirichlet Problem with $p$-Laplacian

TL;DR

This paper establishes the existence of ground state solutions for a Kirchhoff-type fractional p-Laplacian Dirichlet problem using critical point theory and the Nehari method.

Contribution

It introduces a novel approach to proving existence of solutions for fractional Kirchhoff problems with p-Laplacian operators.

Findings

Existence of ground state solutions proven

Application of Nehari method to fractional operators

Extension to Kirchhoff-type fractional problems

Abstract

We consider the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the Nehari method in critical point theory, we obtain the existence theorem of ground state solutions for such Dirichlet problem.