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Locating the peaks of the least energy solutions to an ellyptic system with Neumann boundary conditions
Authors:Angela Pistoia  Miguel Ramos
Institution:a Dipartimento Me. Mo. Mat., Università “La Sapienza”, Via Scarpa 16, 00161-Roma, Italy
b CMAF and Faculty of Sciences, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003-Lisboa, Portugal
Abstract:We consider a system of the form View the MathML source in Ω with Neumann boundary condition on ∂Ω, where Ω is a smooth bounded domain in View the MathML source and f,g are power-type nonlinearities having superlinear and subcritical growth at infinity. We prove that the least energy solutions to such a system concentrate, as ε goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary of Ω.
Keywords:Superlinear elliptic systems  Spike-layered solutions  Positive solutions  Minimax methods
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