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 , \quad u\in W^{2,p}_0(\Omega). \end{align*} By means of the variational approach, we prove that the above problem admits a nontrivial solution.

MSC: 35J60, 35D05, 35J20, 35J40

Pages:  277$-$283     

Volume  71 ,  Issue  3 ,  2019