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$$\begin{array}{r}\mathrm{\Delta }(|\mathrm{\Delta }u{|}^{p-2}\mathrm{\Delta }u)-\lambda \frac{|u{|}^{p-2}u}{|x{|}^{2p}}=\mu h(x)|u{|}^{q-2}u+|u{|}^{p^{\ast }-2}u\text{in }\mathrm{\Omega },\text{quadu}\in W_0^{2,p}(\mathrm{\Omega }).\end{array}$$By means of the variational approach, we prove that theabove problem admits a nontrivial solution.