LEAST ENERGY SOLUTIONS FOR CRITICAL GROWTH EQUATIONS WITH A LOWER ORDER PERTURBATION

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 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.