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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2016
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2016_n_p_Terra http://hdl.handle.net/20.500.12110/paper_10726691_v2016_n_p_Terra |
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| Sumario: | 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. |
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