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...
| Main Authors: | , |
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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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |