A weighted Trudinger-Moser type inequality and its applications to quasilinear elliptic problems with critical growth in the whole Euclidean space

Abstract

We establish a version of the Trudinger-Moser inequality involving unbounded or decaying radial weights in weighted Sobolev spaces. In the light of this inequality and using a minimax procedure we also study existence of solutions for a class of quasilinear elliptic problems involving exponential critical growth.