The Gelfand problem for the 1-homogeneous p-Laplacian

In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain ω ⊃ ℝ N , that is, we deal with (equation presented) in ω with u = 0 on δ ω. For this problem we show that, for p ϵ [2, ∞], there exists a positive critical value...

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Autores principales:	Tapia, J.C., Salas, A.M., Rossi, J.D.
Formato:	JOUR
Materias:	elliptic equations Gelfand problem viscosity solutions
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_21919496_v8_n1_p545_Tapia2023-10-03T16:40:19Z The Gelfand problem for the 1-homogeneous p-Laplacian Tapia, J.C. Salas, A.M. Rossi, J.D. elliptic equations Gelfand problem viscosity solutions In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain ω ⊃ ℝ N , that is, we deal with (equation presented) in ω with u = 0 on δ ω. For this problem we show that, for p ϵ [2, ∞], there exists a positive critical value λ ∗ = λ ∗ (ω, N, p) such that the following holds: • If λ λ ∗ , the problem admits a minimal positive solution wλ ∗ • If λ > λ ∗ , the problem admits no solution. Moreover, the branch of minimal solutions {wλ} is increasing with λ ∗ In addition, using degree theory, for fixed p we show that there exists an unbounded continuum of solutions that emanates from the trivial solution u = 0 with λ = 0, and for a small fixed λ we also obtain a continuum of solutions with p ϵ [2, ∞]. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia
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 Gelfand problem viscosity solutions
spellingShingle	elliptic equations Gelfand problem viscosity solutions Tapia, J.C. Salas, A.M. Rossi, J.D. The Gelfand problem for the 1-homogeneous p-Laplacian
topic_facet	elliptic equations Gelfand problem viscosity solutions
description	In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain ω ⊃ ℝ N , that is, we deal with (equation presented) in ω with u = 0 on δ ω. For this problem we show that, for p ϵ [2, ∞], there exists a positive critical value λ ∗ = λ ∗ (ω, N, p) such that the following holds: • If λ λ ∗ , the problem admits a minimal positive solution wλ ∗ • If λ > λ ∗ , the problem admits no solution. Moreover, the branch of minimal solutions {wλ} is increasing with λ ∗ In addition, using degree theory, for fixed p we show that there exists an unbounded continuum of solutions that emanates from the trivial solution u = 0 with λ = 0, and for a small fixed λ we also obtain a continuum of solutions with p ϵ [2, ∞]. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.
format	JOUR
author	Tapia, J.C. Salas, A.M. Rossi, J.D.
author_facet	Tapia, J.C. Salas, A.M. Rossi, J.D.
author_sort	Tapia, J.C.
title	The Gelfand problem for the 1-homogeneous p-Laplacian
title_short	The Gelfand problem for the 1-homogeneous p-Laplacian
title_full	The Gelfand problem for the 1-homogeneous p-Laplacian
title_fullStr	The Gelfand problem for the 1-homogeneous p-Laplacian
title_full_unstemmed	The Gelfand problem for the 1-homogeneous p-Laplacian
title_sort	gelfand problem for the 1-homogeneous p-laplacian
url	http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia
work_keys_str_mv	AT tapiajc thegelfandproblemforthe1homogeneousplaplacian AT salasam thegelfandproblemforthe1homogeneousplaplacian AT rossijd thegelfandproblemforthe1homogeneousplaplacian AT tapiajc gelfandproblemforthe1homogeneousplaplacian AT salasam gelfandproblemforthe1homogeneousplaplacian AT rossijd gelfandproblemforthe1homogeneousplaplacian
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The Gelfand problem for the 1-homogeneous p-Laplacian

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