A remark on the existence of large solutions via sub and supersolutions
We study the boundary blow-up elliptic problem $Delta u=a(x) f(u)$ in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $u|_{partialOmega}=+infty$. Under suitable growth assumptions on $a$ near $partialOmega$ and on $f$ both at zero and at infinity, we prove the existence of at least a positiv...
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| Format: | Article |
| Language: | English |
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Texas State University
2003-11-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/110/abstr.html |
| Summary: | We study the boundary blow-up elliptic problem $Delta u=a(x) f(u)$ in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $u|_{partialOmega}=+infty$. Under suitable growth assumptions on $a$ near $partialOmega$ and on $f$ both at zero and at infinity, we prove the existence of at least a positive solution. Our proof is based on the method of sub and supersolutions, which permits on the one hand oscillatory behaviour of $f(u)$ at infinity and on the other hand positive weights $a(x)$ which are unbounded and/or oscillatory near the boundary. |
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| ISSN: | 1072-6691 |