Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight

Abstract

In this article we consider the problem $$\displaylines{ -\hbox{div}\big(p(x)\nabla u\big)=|u|^{2^{*}-2}u+\lambda f\quad \text{in }\Omega \cr u=0 \quad \text{on }\partial\Omega }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study the relationship between the behavior of p near its minima on the existence of solutions.

Keywords

• Critical Sobolev exponent
• Nehari manifold
• variational principle