Geodesic
Simplicity and stability of the first eigenvalue of a \((p;q)\) Laplacian system
Electronic journal of differential equations, Tome 2012 (2012)
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 $\mathbb{R}^{N}$.
Classification : 35J60, 35B30, 35B40
Keywords: eigenvalue problem, quasilinear operator, simplicity, stability 
@article{EJDE_2012__2012__a28,
     author = {Afrouzi,  Ghasem A. and Mirzapour,  Maryam and Zhang,  Qihu},
     title = {Simplicity and stability of the first eigenvalue of a \((p;q)\) {Laplacian} system},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1238.35079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a28/}
}
TY  - JOUR
AU  - Afrouzi,  Ghasem A.
AU  - Mirzapour,  Maryam
AU  - Zhang,  Qihu
TI  - Simplicity and stability of the first eigenvalue of a \((p;q)\) Laplacian system
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a28/
LA  - en
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%0 Journal Article
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%A Mirzapour,  Maryam
%A Zhang,  Qihu
%T Simplicity and stability of the first eigenvalue of a \((p;q)\) Laplacian system
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a28/
%G en
%F EJDE_2012__2012__a28
Afrouzi,  Ghasem A.; Mirzapour,  Maryam; Zhang,  Qihu. Simplicity and stability of the first eigenvalue of a \((p;q)\) Laplacian system. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a28/