Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system
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 $$displaylines{ -Delta_p u = lambda |u|^{alpha-1}|v|^{eta-1}v quad hbox{in } Omega,cr -Delta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/08/abstr.html |
| Summary: | This article concerns special properties of the principal eigenvalue of a nonlinear elliptic system with Dirichlet boundary conditions. In particular, we show the simplicity of the first eigenvalue of $$displaylines{ -Delta_p u = lambda |u|^{alpha-1}|v|^{eta-1}v quad hbox{in } Omega,cr -Delta_q v = lambda |u|^{alpha-1}|v|^{eta-1}u quad hbox{in } Omega,cr (u,v)in W_{0}^{1,p}(Omega)imes W_{0}^{1,q}(Omega), }$$ with respect to the exponents p and q, where $Omega$ is a bounded domain in $mathbb{R}^{N}$. |
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| ISSN: | 1072-6691 |