Stable solutions for equations with a quadratic gradient term
We consider positive solutions to the non-variational family of Equations-△u-b(x)|∇u|2=λg(u) in Ω where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ℝn is a bounded smooth domain. We introduce the definition of stability for non-variational problems and...
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todo:paper_10726691_v2016_n_p_Terra2023-10-03T16:02:50Z Stable solutions for equations with a quadratic gradient term Terra, J. Non-variational problem Stable solution We consider positive solutions to the non-variational family of Equations-△u-b(x)|∇u|2=λg(u) in Ω where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ℝn is a bounded smooth domain. We introduce the definition of stability for non-variational problems and establish existence and regularity results for stable solutions. These results generalize the classical results obtained when b(x) = b is a constant function making the problem variational after a suitable transformation. © 2016 Texas State University. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10726691_v2016_n_p_Terra |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Non-variational problem Stable solution |
| spellingShingle |
Non-variational problem Stable solution Terra, J. Stable solutions for equations with a quadratic gradient term |
| topic_facet |
Non-variational problem Stable solution |
| description |
We consider positive solutions to the non-variational family of Equations-△u-b(x)|∇u|2=λg(u) in Ω where λ ≥ 0, b(x) is a given function, g is an increasing nonlinearity with g(0) > 0 and Ω ℝn is a bounded smooth domain. We introduce the definition of stability for non-variational problems and establish existence and regularity results for stable solutions. These results generalize the classical results obtained when b(x) = b is a constant function making the problem variational after a suitable transformation. © 2016 Texas State University. |
| format |
JOUR |
| author |
Terra, J. |
| author_facet |
Terra, J. |
| author_sort |
Terra, J. |
| title |
Stable solutions for equations with a quadratic gradient term |
| title_short |
Stable solutions for equations with a quadratic gradient term |
| title_full |
Stable solutions for equations with a quadratic gradient term |
| title_fullStr |
Stable solutions for equations with a quadratic gradient term |
| title_full_unstemmed |
Stable solutions for equations with a quadratic gradient term |
| title_sort |
stable solutions for equations with a quadratic gradient term |
| url |
http://hdl.handle.net/20.500.12110/paper_10726691_v2016_n_p_Terra |
| work_keys_str_mv |
AT terraj stablesolutionsforequationswithaquadraticgradientterm |
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1807322712884903936 |