AN EXISTENCE RESULT FOR A CLASS OF $p$-BIHARMONIC PROBLEM INVOLVING CRITICAL NONLINEARITY

Abstract

This paper is concerned with the following elliptic equation with Hardy potential and critical Sobolev exponent\begin{align*}\Delta(|\Delta u|^{p-2}\Delta u)-\lambda \frac{|u|^{p-2}u}{|x|^{2p}}=\mu h(x)|u|^{q-2}u+|u|^{p^{*}-2}u\quad\text{in }\Omega , \quadu\in W^{2,p}_0(\Omega).\end{align*}By means of the variational approach, we prove that theabove problem admits a nontrivial solution.