`a`

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

Pages: 151 - 160, Issue Special, September 2009

 Abstract        Full Text (4502.6K)              

Xianjin Chen - Department of Mathematics, Texas A&M University, College Station, TX 77843, United States (email)
Jianxin Zhou - Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States (email)

Abstract: 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:  Cooperative systems, min-orthogonal method, multiple solutions
Mathematics Subject Classification:  Primary: 35A40, 35A15; Secondary: 58E05

Received: July 2008;      Revised: May 2009;      Published: September 2009.