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The Gelfand problem for the 1-homogeneous p-Laplacian
dc.contributor.author | Carmona Tapia, José | |
dc.contributor.author | Molino Salas, Alexis | |
dc.contributor.author | Rossi, Julio D. | |
dc.date.accessioned | 2020-03-02T11:54:34Z | |
dc.date.available | 2020-03-02T11:54:34Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Tapia, J. C., Salas, A. M., & Rossi, J. D. (2019). The Gelfand problem for the 1-homogeneous p-Laplacian. Advances in Nonlinear Analysis, 8(1), 545-558. | es_ES |
dc.identifier.uri | http://hdl.handle.net/10481/59925 | |
dc.description.abstract | 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 ⊂ ℝN, that is, we deal with − 1 p − 1|∇u|2−p div(|∇u|p−2∇u) = λeu in Ω with u = 0 on ∂Ω. For this problem we show that, for p ∈ [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 ∈ [2, ∞]. | es_ES |
dc.description.sponsorship | The first author was partially supported by MINECO–FEDER Grant MTM2015-68210-P (Spain) and Junta de Andalucía FQM-194 (Spain). The second author was partially supported by MINECO–FEDER Grant MTM2015-68210-P (Spain), Junta de Andalucía FQM-116 (Spain) and MINECO Grant BES-2013- 066595 (Spain). The third author was partially supported by CONICET (Argentina) and MINECO–FEDER Grant MTM2015-70227-P (Spain). | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Walter de Gruyter GmbH | es_ES |
dc.rights | Atribución 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | Gelfand problem | es_ES |
dc.subject | Elliptic equations | es_ES |
dc.subject | Viscosity solutions | es_ES |
dc.title | The Gelfand problem for the 1-homogeneous p-Laplacian | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.identifier.doi | 10.1515/anona-2016-0233 |