%0 Journal Article
%T $(N,q)$-Laplacian problems with critical Trudinger-Moser nonlinearities
%A Yang Yang
%A Kanishka Perera
%J Mathematics
%D 2014
%I arXiv
%X We obtain nontrivial solutions of a $(N,q)$-Laplacian problem with a critical Trudinger-Moser nonlinearity in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical nonlinearities, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais-Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.
%U http://arxiv.org/abs/1411.2198v4