Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 08, pp. 1-6.

Title: Simplicity and stability of the first eigenvalue 
       of a (p;q) Laplacian system

Authors: Ghasem A. Afrouzi (Univ. of Mazandaran, Babolsar, Iran)
         Maryam Mirzapour  (Univ. of Mazandaran, Babolsar, Iran)
	 Qihu Zhang (Zhengzhou Univ. of Light Industry, Henan, China)

Abstract:
 This article concerns special properties of the principal
 eigenvalue of a nonlinear elliptic system with
 Dirichlet boundary conditions. In particular, we show
 the simplicity of the first eigenvalue of
 $$\displaylines{
 -\Delta_p u = \lambda |u|^{\alpha-1}|v|^{\beta-1}v \quad
 \hbox{in } \Omega,\cr
 -\Delta_q v = \lambda |u|^{\alpha-1}|v|^{\beta-1}u
 \quad \hbox{in } \Omega,\cr
 (u,v)\in W_{0}^{1,p}(\Omega)\times W_{0}^{1,q}(\Omega),
 }$$
 with respect to the exponents p and q, where $\Omega$ is
 a bounded domain in $\mathbb{R}^{N}$.

Submitted November 3, 2011. Published January 12, 2012.
Math Subject Classifications: 35J60, 35B30, 35B40.
Key Words: Eigenvalue problem; quasilinear operator;
           simplicity; stability.