Singular $p$-biharmonic problem with the Hardy potential

TL;DR

This paper investigates the existence and multiplicity of solutions for a singular $p$-biharmonic problem involving Hardy potential using variational and Nehari manifold methods.

Contribution

It introduces new existence and multiplicity results for a singular $p$-biharmonic problem with Hardy potential, combining monotonicity, variational, and Nehari manifold techniques.

Findings

Existence of solutions established using variational methods.

Multiple solutions proved via Nehari manifold approach.

An example illustrates the applicability of the results.

Abstract

The aim of this paper is to study existence results for a singular problem involving the $p$-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, the multiplicity of solutions is proved. An example is also given, to illustrate the importance of these results.