Electron. J. Diff. Equ., Vol. 2012 (2012), No. 08, pp. 1-6.

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

Ghasem A. Afrouzi, Maryam Mirzapour, Qihu Zhang

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.

An addendum was posted on July 21, 2016. It states that some parts were copied from reference [6] without mentioning the source. See the last page of this article.

Show me the PDF file (195 KB), TEX file, and other files for this article.

Ghasem Alizadeh Afrouzi
Department of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: afrouzi@umz.ac.ir
Maryam Mirzapour
Department of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email mirzapour@stu.umz.ac.ir
  Qihu Zhang
Department of Mathematics and Information Science
Zhengzhou University of Light Industry
Zhengzhou, Henan 450002, China
email: zhangqh1999@yahoo.com.cn

Return to the EJDE web page