Orateur
Asma Benhamida
Description
Consider the problem $-div(\alpha(x)|\nabla u|^{p-2}\nabla u)=\lambda |u|^{q-2}u+|u|^{p^{\star}-2}u$ in a bounded domain, with
homogeneous Dirichlet boundary condition, where $\alpha(.)$ is a continuous function, $p^{*}$ the Sobolev critical exponent and $2\leq p\leq q< p^{*}$. We prove the existence of positive solutions which depends, among others, on the behavior of the potential $\alpha(.)$ in the neighborhood of its minima, the position of $p^{2}$ with respect to dimension of the space and the position of $q$ with respect to specific values.
