Positive solutions to nonlinear elliptic problems involving Sobolev exponent

Carlo Mercuri, Riccardo Molle

In this paper we consider nonlinear elliptic PDEs of the type $$-Δ_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }Ω,$$ where $1<p<N$ and $p^{\ast }=Np/(N-p)$ is the critical Sobolev e…