A diffusion equation with a variable reaction order

This paper deals with the problem (Formula presented) where Ω R N is a bounded smooth domain, λ > 0 is a parameter and the reaction order q(x) is a Hölder continuous positive function satisfying q(x) > 1 for all x ò . The relevant feature here is that q is assumed to achieve the value...

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Detalles Bibliográficos
Publicado: 2018
Materias:
A Priori Estimates
Palais-Smale Sequences
Variational Methods
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n3_p555_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_15361365_v18_n3_p555_GarciaMelian
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15361365_v18_n3_p555_GarciaMelian
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spelling paper:paper_15361365_v18_n3_p555_GarciaMelian2023-06-08T16:20:11Z A diffusion equation with a variable reaction order A Priori Estimates Palais-Smale Sequences Variational Methods This paper deals with the problem (Formula presented) where Ω R N is a bounded smooth domain, λ > 0 is a parameter and the reaction order q(x) is a Hölder continuous positive function satisfying q(x) > 1 for all x ò . The relevant feature here is that q is assumed to achieve the value one on ∂Ω. By assuming that q is subcritical, our main result states the existence of a positive solution for all λ > 0. We also study its asymptotic behavior as λ→ 0 and as λ→ ∞. It should be noticed that the fact that q = 1 somewhere in ∂Ω gives rise to serious difficulties when looking for critical points of the functional associated with the problem above. This work is a continuation of [13] where q is assumed to take values both greater and smaller than one in , but is constrained to satisfy q(x) > 1 on ∂Ω. © 2018 Walter de Gruyter GmbH, Berlin/Boston. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n3_p555_GarciaMelian http://hdl.handle.net/20.500.12110/paper_15361365_v18_n3_p555_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 A Priori Estimates
Palais-Smale Sequences
Variational Methods
spellingShingle A Priori Estimates
Palais-Smale Sequences
Variational Methods
A diffusion equation with a variable reaction order
topic_facet A Priori Estimates
Palais-Smale Sequences
Variational Methods
description This paper deals with the problem (Formula presented) where Ω R N is a bounded smooth domain, λ > 0 is a parameter and the reaction order q(x) is a Hölder continuous positive function satisfying q(x) > 1 for all x ò . The relevant feature here is that q is assumed to achieve the value one on ∂Ω. By assuming that q is subcritical, our main result states the existence of a positive solution for all λ > 0. We also study its asymptotic behavior as λ→ 0 and as λ→ ∞. It should be noticed that the fact that q = 1 somewhere in ∂Ω gives rise to serious difficulties when looking for critical points of the functional associated with the problem above. This work is a continuation of [13] where q is assumed to take values both greater and smaller than one in , but is constrained to satisfy q(x) > 1 on ∂Ω. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
title A diffusion equation with a variable reaction order
title_short A diffusion equation with a variable reaction order
title_full A diffusion equation with a variable reaction order
title_fullStr A diffusion equation with a variable reaction order
title_full_unstemmed A diffusion equation with a variable reaction order
title_sort diffusion equation with a variable reaction order
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v18_n3_p555_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_15361365_v18_n3_p555_GarciaMelian
_version_ 1768543292745580544

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