Publicação: Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth
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2015-04-07
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Texas State University
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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 (del u/root 1+vertical bar del u vertical bar(2)) = lambda vertical bar u vertical bar(q-2) u + vertical bar u vertical bar(2*-2)u in Omegau = 0 on partial derivative Omega,where Omega is a bounded smooth domain of R-N, 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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Electronic Journal Of Differential Equations. San Marcos: Texas State University, p. 1-18, 2015.
