Abstract
We study existence and nonexistence of least energy solutions of a quasilinear critical growth equation with degenerate $m$-Laplace operator in a bounded domain in $\mathbb{R}^n$ with $n>m>1$. Existence and nonexistence of solutions of this problem depend on a lower order perturbation and on the space dimension $n$. Our proofs are obtained with critical point theory and the lack of compactness, due to critical growth condition, is overcome by constructing minimax levels in a suitable compactness range.
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