Locating the peaks of the least energy solutions to an ellyptic system with Neumann boundary conditions |
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Authors: | Angela Pistoia Miguel Ramos |
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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 |
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Abstract: | We consider a system of the form in Ω with Neumann boundary condition on ∂Ω, where Ω is a smooth bounded domain in 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. |
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Keywords: | Superlinear elliptic systems Spike-layered solutions Positive solutions Minimax methods |
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