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Spike-layered solutions for an elliptic system with Neumann boundary conditions
Authors:Miguel Ramos   Jianfu Yang
Affiliation:CMAF and Faculty of Sciences, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal ; Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P.O. Box 71010, Wuhan, Hubei 430071 People's Republic of China
Abstract:We prove the existence of nonconstant positive solutions for a system of the form $-varepsilon^2Delta u + u = g(v)$, $-varepsilon^2Delta v + v = f(u)$ in $Omega$, with Neumann boundary conditions on $partial Omega$, where $Omega$ is a smooth bounded domain and $f$, $g$are power-type nonlinearities having superlinear and subcritical growth at infinity. For small values of $varepsilon$, the corresponding solutions $u_{varepsilon}$ and $v_{varepsilon}$ admit a unique maximum point which is located at the boundary of $Omega$.

Keywords:Superlinear elliptic systems   spike-layered solutions   positive solutions   minimax methods
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