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
Autores principales:	García-Melián, J., Rossi, J.D., De Lis, J.C.S.
Formato:	JOUR
Materias:	A Priori Estimates Palais-Smale Sequences Variational Methods
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_15361365_v18_n3_p555_GarciaMelian
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_15361365_v18_n3_p555_GarciaMelian
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spelling	todo:paper_15361365_v18_n3_p555_GarciaMelian2023-10-03T16:21:49Z A diffusion equation with a variable reaction order García-Melián, J. Rossi, J.D. De Lis, J.C.S. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 García-Melián, J. Rossi, J.D. De Lis, J.C.S. 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.
format	JOUR
author	García-Melián, J. Rossi, J.D. De Lis, J.C.S.
author_facet	García-Melián, J. Rossi, J.D. De Lis, J.C.S.
author_sort	García-Melián, J.
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
url	http://hdl.handle.net/20.500.12110/paper_15361365_v18_n3_p555_GarciaMelian
work_keys_str_mv	AT garciamelianj adiffusionequationwithavariablereactionorder AT rossijd adiffusionequationwithavariablereactionorder AT delisjcs adiffusionequationwithavariablereactionorder AT garciamelianj diffusionequationwithavariablereactionorder AT rossijd diffusionequationwithavariablereactionorder AT delisjcs diffusionequationwithavariablereactionorder
_version_	1782031044458840064

A diffusion equation with a variable reaction order

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