The sublinear problem for the $1$-homogeneous $p$-Laplacian
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- by Pedro J. Martínez-Aparicio, Mayte Pérez-Llanos and Julio D. Rossi PDF
- Proc. Amer. Math. Soc. 142 (2014), 2641-2648 Request permission
Abstract:
In this paper we prove the existence and uniqueness of a positive viscosity solution of the $1$-homogeneous $p$-Laplacian with a sublinear right-hand side; that is, $-|D u|^{2-p}\textrm {div}\:(|D u|^{p-2}Du)=\lambda u^q$ in $\Omega$, $u=0$ on $\partial \Omega$, where $\Omega$ is a bounded starshaped domain, $\lambda >0$, $p>2$ and $0<q<1$.References
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Additional Information
- Pedro J. Martínez-Aparicio
- Affiliation: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202, Murcia, Spain
- Email: pedroj.martinez@upct.es
- Mayte Pérez-Llanos
- Affiliation: Departamento de Matemáticas, Campus de Cantoblanco, Universidad Autonoma de Madrid, 28049, Madrid, Spain
- Email: mayte.perez@uam.es
- Julio D. Rossi
- Affiliation: Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain (on leave from Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina)
- MR Author ID: 601009
- ORCID: 0000-0001-7622-2759
- Email: julio.rossi@ua.es
- Received by editor(s): September 23, 2011
- Published electronically: April 21, 2014
- Additional Notes: The first author was supported by MICINN Ministerio de Ciencia e Innovacion (Spain) MTM2009-10878 and Junta de Andalucia FQM-116
The second and third authors were supported by project MTM2010-18128 (Spain) - Communicated by: James E. Colliander
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 2641-2648
- MSC (2010): Primary 35A02, 35B51, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-2014-12108-3
- MathSciNet review: 3209320