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 $$displaylines{ -Delta_p u = lambda |u|^{alpha-1}|v|^{eta-1}v quad hbox{in } Omega,cr -Delta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/08/abstr.html |
| _version_ | 1818755717064032256 |
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| author | Ghasem A. Afrouzi Maryam Mirzapour Qihu Zhang |
| author_facet | Ghasem A. Afrouzi Maryam Mirzapour Qihu Zhang |
| author_sort | Ghasem A. Afrouzi |
| collection | DOAJ |
| description | This article concerns special properties of the principal eigenvalue of a nonlinear elliptic system with Dirichlet boundary conditions. In particular, we show the simplicity of the first eigenvalue of $$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), }$$ with respect to the exponents p and q, where $Omega$ is a bounded domain in $mathbb{R}^{N}$. |
| first_indexed | 2024-12-18T05:43:35Z |
| format | Article |
| id | doaj.art-3991f932f0e34a4c9c4d883cd0d31efc |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T05:43:35Z |
| publishDate | 2012-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3991f932f0e34a4c9c4d883cd0d31efc2022-12-21T21:19:06ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-01-01201208,16Simplicity and stability of the first eigenvalue of a (p;q) Laplacian systemGhasem A. AfrouziMaryam MirzapourQihu ZhangThis article concerns special properties of the principal eigenvalue of a nonlinear elliptic system with Dirichlet boundary conditions. In particular, we show the simplicity of the first eigenvalue of $$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 $mathbb{R}^{N}$.http://ejde.math.txstate.edu/Volumes/2012/08/abstr.htmlEigenvalue problemquasilinear operatorsimplicitystability |
| spellingShingle | Ghasem A. Afrouzi Maryam Mirzapour Qihu Zhang Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system Electronic Journal of Differential Equations Eigenvalue problem quasilinear operator simplicity stability |
| title | Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system |
| title_full | Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system |
| title_fullStr | Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system |
| title_full_unstemmed | Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system |
| title_short | Simplicity and stability of the first eigenvalue of a (p;q) Laplacian system |
| title_sort | simplicity and stability of the first eigenvalue of a p q laplacian system |
| topic | Eigenvalue problem quasilinear operator simplicity stability |
| url | http://ejde.math.txstate.edu/Volumes/2012/08/abstr.html |
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