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On the nonhomogeneous Neumann problem with weight and with critical nonlinearity in the boundary

Abstract : We consider the problem: -div(p(x)del u)=lambda u-f(x) in Omega, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(2/N-2)u on partial derivative Omega is a bounded smooth domain in R-N, N >= 3. Under some conditions on partial derivative Omega, p, Q, f, lambda and the mean curvature at some point x(0), we prove the existence of solutions of the above problem. We use variational arguments, namely Ekeland's variational principle, the min-max principle and the mountain pass theorem. (c) 2006 Elsevier Ltd. All rights reserved.
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Habib Yazidi. On the nonhomogeneous Neumann problem with weight and with critical nonlinearity in the boundary. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2008, 68 (2), pp.329--364. ⟨10.1016/j.na.2006.11.001⟩. ⟨hal-00693078⟩

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