Abstract
In this paper, we establish the existence of a positive ground state solution for a weighted problem under boundary Dirichlet condition in the unit ball of $\mathbb R^N,$ $N > 2$. The nonlinearity of the equation is critical or subcritical growth in view of Trudinger-Moser inequalities. In order to obtain our existence result we used minimax techniques combined with Trudinger-Moser inequalities. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth and we stress its importance to check compactness levels.
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