Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary

In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation - Δu = λ u - u p in Ω, with the nonlinear boundary condition ≈u/≈ν = ur on Ω. Here Ω is a smooth bounded domain of ℝ with outward unit...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Elliptic equations
Nonlinear boundary conditions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v187_n3_p459_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_03733114_v187_n3_p459_GarciaMelian
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03733114_v187_n3_p459_GarciaMelian
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spelling paper:paper_03733114_v187_n3_p459_GarciaMelian2023-06-08T15:37:53Z Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary Rossi, Julio Daniel Elliptic equations Nonlinear boundary conditions In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation - Δu = λ u - u p in Ω, with the nonlinear boundary condition ≈u/≈ν = ur on Ω. Here Ω is a smooth bounded domain of ℝ with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly based on bifurcation techniques, sub-supersolutions and variational methods. © 2007 Springer-Verlag. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v187_n3_p459_GarciaMelian http://hdl.handle.net/20.500.12110/paper_03733114_v187_n3_p459_GarciaMelian
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Elliptic equations
Nonlinear boundary conditions
spellingShingle Elliptic equations
Nonlinear boundary conditions
Rossi, Julio Daniel
Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
topic_facet Elliptic equations
Nonlinear boundary conditions
description In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation - Δu = λ u - u p in Ω, with the nonlinear boundary condition ≈u/≈ν = ur on Ω. Here Ω is a smooth bounded domain of ℝ with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly based on bifurcation techniques, sub-supersolutions and variational methods. © 2007 Springer-Verlag.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
title_short Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
title_full Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
title_fullStr Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
title_full_unstemmed Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
title_sort nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v187_n3_p459_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_03733114_v187_n3_p459_GarciaMelian
work_keys_str_mv AT rossijuliodaniel nonnegativesolutionstoanellipticproblemwithnonlinearabsorptionandanonlinearincomingfluxontheboundary
_version_ 1768542317108527104

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