Geodesic
Simplicity and stability of the first eigenvalue of a $(p;q)$ Laplacian system
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a28/}
}
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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/