Existence and nonexistence of solutions for singular quadratic quasilinear equations
We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $−\Delta u +\frac{|\nabla u|^2}}{u^\gamma} = f$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\O...
| Main Authors: | , , , , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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Elsevier
2011
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| Online Access: | http://hdl.handle.net/10835/360 |
| _version_ | 1789406474555883520 |
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| author | Arcoya, David Carmona Tapia, José Leonori, Tommaso Martínez-Aparicio, Pedro J. Orsina, Luigi Petitta, Francesco |
| author_facet | Arcoya, David Carmona Tapia, José Leonori, Tommaso Martínez-Aparicio, Pedro J. Orsina, Luigi Petitta, Francesco |
| author_sort | Arcoya, David |
| collection | DSpace |
| description | We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $−\Delta u +\frac{|\nabla u|^2}}{u^\gamma} = f$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is an open bounded subset of $\mathbb{R}$, $\gamma > 0$ and $f$ is a function which is strictly positive on every compactly contained subset of $\Omega$. As a consequence of our main results, we prove that the condition $\gamma<2$ is necessary and sufficient for the existence of solutions in $H^1_0(\Omega)$ for every sufficiently regular $f$ as above. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-360 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2011 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-3602023-04-12T19:37:47Z Existence and nonexistence of solutions for singular quadratic quasilinear equations Arcoya, David Carmona Tapia, José Leonori, Tommaso Martínez-Aparicio, Pedro J. Orsina, Luigi Petitta, Francesco Matemáticas We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $−\Delta u +\frac{|\nabla u|^2}}{u^\gamma} = f$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is an open bounded subset of $\mathbb{R}$, $\gamma > 0$ and $f$ is a function which is strictly positive on every compactly contained subset of $\Omega$. As a consequence of our main results, we prove that the condition $\gamma<2$ is necessary and sufficient for the existence of solutions in $H^1_0(\Omega)$ for every sufficiently regular $f$ as above. 2011-11-09T12:11:39Z 2011-11-09T12:11:39Z 2009 info:eu-repo/semantics/article J. Differential Equations 246 (2009) 4006–4042 http://hdl.handle.net/10835/360 en http://dx.doi.org/10.1016/j.jde.2009.01.016 info:eu-repo/semantics/openAccess Elsevier |
| spellingShingle | Matemáticas Arcoya, David Carmona Tapia, José Leonori, Tommaso Martínez-Aparicio, Pedro J. Orsina, Luigi Petitta, Francesco Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title | Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title_full | Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title_fullStr | Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title_full_unstemmed | Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title_short | Existence and nonexistence of solutions for singular quadratic quasilinear equations |
| title_sort | existence and nonexistence of solutions for singular quadratic quasilinear equations |
| topic | Matemáticas |
| url | http://hdl.handle.net/10835/360 |
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