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Spike-layered solutions for an elliptic system with Neumann boundary conditions

Authors:	Miguel Ramos Jianfu Yang

Institution:	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 $-\varepsilon^2\Delta u + u = g(v)$ , $-\varepsilon^2\Delta v + v = f(u)$ in $\Omega$ , with Neumann boundary conditions on $\partial \Omega$ , where $\Omega$ is a smooth bounded domain and , 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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