Singular $p$-biharmonic problems involving the Hardy-Sobolev exponent

TL;DR

This paper investigates the existence and multiplicity of solutions for singular p-biharmonic problems with Hardy potential and critical Hardy-Sobolev exponent using variational methods, providing theoretical results and an illustrative example.

Contribution

It introduces new existence and multiplicity results for singular p-biharmonic problems involving Hardy-Sobolev exponents using advanced variational techniques.

Findings

Existence of solutions established via Mountain pass theorem.

Multiple solutions demonstrated through variational principles.

An illustrative example confirms the theoretical results.

Abstract

This paper is concerned with existence results for the singular $p$-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. More precisely, by using variational methods combined with the Mountain pass theorem and the Ekeland variational principle, we establish the existence and multiplicity of solutions. To illustrate the usefulness of our results, an illustrative example is also presented.