Positive solutions for a class of singular elliptic system
In this paper, we mainly study the existence, boundary behavior and uniqueness of solutions for the following singular elliptic systems involving weights $-\triangle u =w(x)u^{-p}v^{-q}, -\triangle v =\lambda(x)u^{-r}v^{-s}, u>0, v>0, \ x\in \Omega, \ u|_{\partial \Omega}=v|_{\partial \Omeg...
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| Format: | Article |
| Language: | English |
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University of Szeged
2017-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5570 |
| _version_ | 1797830578068783104 |
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| author | Ling Mi |
| author_facet | Ling Mi |
| author_sort | Ling Mi |
| collection | DOAJ |
| description | In this paper, we mainly study the existence, boundary behavior and uniqueness of solutions for the following singular elliptic systems involving weights $-\triangle u =w(x)u^{-p}v^{-q}, -\triangle v =\lambda(x)u^{-r}v^{-s}, u>0, v>0, \ x\in \Omega, \ u|_{\partial \Omega}=v|_{\partial \Omega}=0$, where $\Omega$ is a bounded domain with a smooth boundary in $\mathbb R^N\ (N\geq 2)$, $p, s \geq 0,$ $q, r > 0$ and the weight functions $w(x), \lambda(x) \in C^{\alpha}(\bar{\Omega})$ which are positive in $\Omega$ and may be blow-up on the boundary. |
| first_indexed | 2024-04-09T13:38:18Z |
| format | Article |
| id | doaj.art-5cf18cd94c2846a1ba6e84b1230138c4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:18Z |
| publishDate | 2017-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-5cf18cd94c2846a1ba6e84b1230138c42023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-04-0120172411310.14232/ejqtde.2017.1.245570Positive solutions for a class of singular elliptic systemLing Mi0School of Science, Linyi University, Linyi, Shandong, P.R. ChinaIn this paper, we mainly study the existence, boundary behavior and uniqueness of solutions for the following singular elliptic systems involving weights $-\triangle u =w(x)u^{-p}v^{-q}, -\triangle v =\lambda(x)u^{-r}v^{-s}, u>0, v>0, \ x\in \Omega, \ u|_{\partial \Omega}=v|_{\partial \Omega}=0$, where $\Omega$ is a bounded domain with a smooth boundary in $\mathbb R^N\ (N\geq 2)$, $p, s \geq 0,$ $q, r > 0$ and the weight functions $w(x), \lambda(x) \in C^{\alpha}(\bar{\Omega})$ which are positive in $\Omega$ and may be blow-up on the boundary.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5570singular elliptic systemsdirichlet problemsexistenceboundary behavioruniqueness |
| spellingShingle | Ling Mi Positive solutions for a class of singular elliptic system Electronic Journal of Qualitative Theory of Differential Equations singular elliptic systems dirichlet problems existence boundary behavior uniqueness |
| title | Positive solutions for a class of singular elliptic system |
| title_full | Positive solutions for a class of singular elliptic system |
| title_fullStr | Positive solutions for a class of singular elliptic system |
| title_full_unstemmed | Positive solutions for a class of singular elliptic system |
| title_short | Positive solutions for a class of singular elliptic system |
| title_sort | positive solutions for a class of singular elliptic system |
| topic | singular elliptic systems dirichlet problems existence boundary behavior uniqueness |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5570 |
| work_keys_str_mv | AT lingmi positivesolutionsforaclassofsingularellipticsystem |