Combined effects in quasilinear elliptic problems with lack of compactness

Abstract

We are concerned with the study of weak solutions to a class of subcritical quasilinear elliptic equations with weight, variable parameter, and lack of compactness. By means of variational methods, we establish that this problem does not have any solution if the positive parameter is small enough, while at least two distinct solutions exist, provided that the parameter is sufficiently large.