A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems

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2009, 2009(Special): 151-160. doi: 10.3934/proc.2009.2009.151

A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems

1.	Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
2.	Department of Mathematics, Texas A&M University, College Station, TX 77843-3368

Received July 2008 Revised May 2009 Published September 2009

Abstract
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The aim of this paper is to numerically investigate multiple solutions of semilinear elliptic systems with zero Dirichlet boundary conditions

-$\Delta u=F_u(x;u,v),$ $x\in\Omega,
-$\Delta v=F_v(x;u,v),$ $x\in\Omega,

where $\Omega \subset \mathbb{R}^{N}$ ($N\ge 1$) is a bounded domain. A strongly coupled case where the potential $F(x;u,v)$ takes the form $|u|^{\alpha_1}|v|^{\alpha_2}$ with $\alpha_1, \alpha_2>1$ is specially studied. By using a local min-orthogonal method, both positive and sign-changing solutions are found and displayed.

Keywords: min-orthogonal method, Cooperative systems, multiple solutions.

Mathematics Subject Classification: Primary: 35A40, 35A15; Secondary: 58E05.

Citation: Xianjin Chen, Jianxin Zhou. A local min-orthogonal method for multiple solutions of strongly coupled elliptic systems. Conference Publications, 2009, 2009 (Special) : 151-160. doi: 10.3934/proc.2009.2009.151

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