    December  2014, 34(12): 5299-5323. doi: 10.3934/dcds.2014.34.5299

Segregated peak solutions of coupled Schrödinger systems with Neumann boundary conditions

 1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875

Received  July 2013 Revised  May 2014 Published  June 2014

We consider the following two coupled Schrödinger systems in a bounded domain $\Omega\subset \mathbb{R}^N(N=2,3)$ with Neumann boundary conditions $$\left\{ \begin{array}{ll} -\epsilon^2 \triangle u + u = \mu_1 u^3+ \beta u v^2,\\ -\epsilon^2 \triangle v + v =\mu_2 v^3+ \beta u^2 v,\\ u>0, v>0, \\ \partial u/\partial n = 0,\partial v/\partial n = 0, \mbox{on } \partial \Omega. \end{array}\right.$$ Suppose the mean curvature $H(P)$ of the boundary $\partial \Omega$ admits several local maximums( or local minimums), we obtain the existence of segregated solutions $(u_\epsilon,v_\epsilon)$ to the above system such that both of $u_\epsilon$ and $v_\epsilon$ admit more than one local maximums, furthermore as $\epsilon$ goes to zero, the maximum points of $u_\epsilon$ and $v_\epsilon$ concentrate at different local maximum points( or local minimum points) of the mean curvature $H(P)$ respectively.
Citation: Zhongwei Tang. Segregated peak solutions of coupled Schrödinger systems with Neumann boundary conditions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 5299-5323. doi: 10.3934/dcds.2014.34.5299
References:
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References:
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