Advanced Search

The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the $N$-Laplacian $$-{\Delta }_{N}u\equiv -{div\left(\right|\nabla u|}^{N-2}\nabla u)=e(x,u)+h\left(x\right)\text{in}\Omega$$ where $u\in W_0^{1,N}\left({ℝ}^N\right)$, $\Omega$ is a bounded smooth domain in ${ℝ}^N$, $N\ge 2$, $e(x,u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h\left(x\right)\in {\left(W_0^{1,N}\right)}^{*}$ is a small perturbation.