Multiple solutions to singular fourth order elliptic equations

TL;DR

This paper establishes the existence of at least two distinct weak solutions for a singular fourth-order elliptic equation with critical Sobolev growth using the Nehari manifold method.

Contribution

It introduces a novel application of the Nehari manifold approach to singular fourth-order elliptic equations with critical growth.

Findings

Proved existence of multiple solutions

Applied Nehari manifold to singular elliptic problems

Addressed critical Sobolev growth challenges

Abstract

Using the method of Nehari manifold, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singulatities and with critical Sobolev growth.