Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth
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In this work we study an existence and multiplicity of solutions for the prescribed mean-curvature problem with critical growth, -div(Formula Presented), where Ω is a bounded smooth domain of RN, N ≥ 3 and 1 < q < 2. To employ variational arguments, we consider an auxiliary problem which is proved to have infinitely many solutions by genus theory. A clever estimate in the gradient of the solutions of the modified problem is necessary to recover solutions of the original problem.
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Critical exponent, Prescribed mean-curvature problem, Variational methods
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Inglês
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Electronic Journal of Differential Equations, v. 2015.
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