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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2019
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21919496_v8_n1_p545_Tapia http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia |
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paper:paper_21919496_v8_n1_p545_Tapia2023-06-08T16:35:05Z The Gelfand problem for the 1-homogeneous p-Laplacian 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. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21919496_v8_n1_p545_Tapia 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 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. |
| 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 |
| publishDate |
2019 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21919496_v8_n1_p545_Tapia http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia |
| _version_ |
1768542909895802880 |