The sub-supersolution method for weak solutions
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- by Marcelo Montenegro and Augusto C. Ponce
- Proc. Amer. Math. Soc. 136 (2008), 2429-2438
- DOI: https://doi.org/10.1090/S0002-9939-08-09231-9
- Published electronically: February 29, 2008
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Abstract:
We extend the method of sub and supersolutions in order to prove existence of $L^1$-solutions of the equation $-\Delta u = f(x,u)$ in $\Omega$, where $f$ is a Carathéodory function. The proof is based on Schauder’s fixed point theorem.References
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Bibliographic Information
- Marcelo Montenegro
- Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brasil
- Email: msm@ime.unicamp.br
- Augusto C. Ponce
- Affiliation: Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 6083) Fédération Denis Poisson, Université François Rabelais 37200, Tours, France
- Email: ponce@lmpt.univ-tours.fr
- Received by editor(s): September 12, 2006
- Published electronically: February 29, 2008
- Communicated by: David S. Tartakoff
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 2429-2438
- MSC (2000): Primary 35D05, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-08-09231-9
- MathSciNet review: 2390510