Large solutions of semilinear elliptic equations with nonlinear gradient terms (Q1970291)
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scientific article; zbMATH DE number 1417985
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Large solutions of semilinear elliptic equations with nonlinear gradient terms |
scientific article; zbMATH DE number 1417985 |
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Large solutions of semilinear elliptic equations with nonlinear gradient terms (English)
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6 December 2000
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The authors show that under suitable assumptions on \(\gamma >1\), \(q>0\), and \(p(x)\) large solutions of the equations \[ \Delta u \pm |\nabla u|^q = p(x) u^\gamma \] exist. Moreover, if \(\gamma \leq 1\) or the continuous function \(p(x)\) has compact support in \(\Omega,\) such solutions do not exist.
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elliptic equations
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non linear equations
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existence
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non-existence
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