Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains
In this study, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$displaylines{ Lu-mu u g_{1} + h(u) g_{2}= fquad hbox{in }Omega,cr u = 0quad hbox{on }partialOmega }$$ in a suitable weighted Sobolev space. Here the domain $Omega...
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| Format: | Article |
| Language: | English |
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Texas State University
2009-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/160/abstr.html |
| _version_ | 1818956832462340096 |
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| author | Venkataramanarao Raghavendra Rasmita Kar |
| author_facet | Venkataramanarao Raghavendra Rasmita Kar |
| author_sort | Venkataramanarao Raghavendra |
| collection | DOAJ |
| description | In this study, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$displaylines{ Lu-mu u g_{1} + h(u) g_{2}= fquad hbox{in }Omega,cr u = 0quad hbox{on }partialOmega }$$ in a suitable weighted Sobolev space. Here the domain $Omegasubsetmathbb{R}^{n}$, $ngeq 3$, is not necessarily bounded, and $h$ is a continuous bounded nonlinearity. The theory is also extended for $h$ continuous and unbounded. |
| first_indexed | 2024-12-20T11:00:13Z |
| format | Article |
| id | doaj.art-4b271bb5b32a43458c1239dba18281b5 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T11:00:13Z |
| publishDate | 2009-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-4b271bb5b32a43458c1239dba18281b52022-12-21T19:43:02ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-12-012009160,17Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domainsVenkataramanarao RaghavendraRasmita KarIn this study, we prove the existence of a weak solution for the degenerate semilinear elliptic Dirichlet boundary-value problem $$displaylines{ Lu-mu u g_{1} + h(u) g_{2}= fquad hbox{in }Omega,cr u = 0quad hbox{on }partialOmega }$$ in a suitable weighted Sobolev space. Here the domain $Omegasubsetmathbb{R}^{n}$, $ngeq 3$, is not necessarily bounded, and $h$ is a continuous bounded nonlinearity. The theory is also extended for $h$ continuous and unbounded.http://ejde.math.txstate.edu/Volumes/2009/160/abstr.htmlDegenerate equationsweighted Sobolev spaceunbounded domain |
| spellingShingle | Venkataramanarao Raghavendra Rasmita Kar Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains Electronic Journal of Differential Equations Degenerate equations weighted Sobolev space unbounded domain |
| title | Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| title_full | Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| title_fullStr | Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| title_full_unstemmed | Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| title_short | Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| title_sort | existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains |
| topic | Degenerate equations weighted Sobolev space unbounded domain |
| url | http://ejde.math.txstate.edu/Volumes/2009/160/abstr.html |
| work_keys_str_mv | AT venkataramanaraoraghavendra existenceofweaksolutionsfordegeneratesemilinearellipticequationsinunboundeddomains AT rasmitakar existenceofweaksolutionsfordegeneratesemilinearellipticequationsinunboundeddomains |