Critical growth quasilinear elliptic problems with shifting subcritical perturbation

Abstract

We consider a family of quasilinear elliptic problems on bounded domains with perturbed critical growth term; we prove the existence of nontrivial solutions when the perturbation depends on a parameter which forces the solutions to have a suitable behavior in order to interact with it. We also study the behavior of the solutions for varying parameter, and we show that concentration phenomena appear as the parameter tends to infinity.