# American Institute of Mathematical Sciences

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

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.

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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