Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains

Abstract

In this paper we study the existence of positive solutions for the problem $$ -Delta_{p}u=u^{p^{*}-1} quad hbox{in } Omega quad hbox{and} quad u=0 quad hbox{on } partial{Omega} $$ where $Omega$ is a perturbed annular domain (see definition in the introduction) and $N greater than p geq 2$. To prove our main results, we use the Concentration-Compactness Principle and variational techniques.

Keywords

• p-Laplacian operator
• critical exponents
• deformation lemma.