Positive solutions for φ-Laplacian equations with discontinuous state-dependent forcing terms
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Título: | Positive solutions for φ-Laplacian equations with discontinuous state-dependent forcing terms |
Autor/a: | Precup, Radu Rodríguez López, Jorge |
Centro/Departamento: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
Palabras chave: | Discontinuous differential equation | φ-Laplacian problem | Positive solution | Fixed point | Multivalued map | Infinitely many solutions | |
Data: | 2019 |
Editor: | Vilnius University Press |
Cita bibliográfica: | PrecupR. and Rodríguez-LópezJ. (2019) “Positive solutions for phi-Laplace equations with discontinuous state-dependent forcing terms”, Nonlinear Analysis: Modelling and Control, 24(3), 447-461. doi: 10.15388/NA.2019.3.8. |
Resumo: | This paper concerns the existence, localization and multiplicity of positive solutions for a -Laplacian problem with a perturbed term that may have discontinuities in the state variable. First, the initial discontinuous differential equation is replaced by a differential inclusion with an upper semicontinuous term. Next, the existence and localization of a positive solution of the inclusion is obtained via a compression-expansion fixed point theorem for a composition of two multivalued maps, and finally, a suitable control of discontinuities allows to prove that any solution of the inclusion is a solution in the sense of Carathéodory of the initial discontinuous equation. No monotonicity assumptions on the nonlinearity are required |
Versión do editor: | https://doi.org/10.15388/NA.2019.3.8 |
URI: | http://hdl.handle.net/10347/21169 |
DOI: | 10.15388/NA.2019.3.8 |
ISSN: | 1392-5113 |
E-ISSN: | 2335-8963 |
Dereitos: | © 2019 Vilnius University. This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/) |
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