On a class of quasilinear elliptic problems with critical exponential growth on the whole space

Abstract

In this paper we prove a kind of weighted Trudinger-Moser inequality which is employed to establish sufficient conditions for the existence of solutions to a large class of quasilinear elliptic differential equations with critical exponential growth. The class of operators considered includes, as particular cases, the Laplace, $p$-Laplace and $k$-Hessian operators when acting on radially symmetric functions.