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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The sub-supersolution method for weak solutions


Authors: Marcelo Montenegro and Augusto C. Ponce
Journal: Proc. Amer. Math. Soc. 136 (2008), 2429-2438
MSC (2000): Primary 35D05, 35J60
Published electronically: February 29, 2008
MathSciNet review: 2390510
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09231-9
PII: S 0002-9939(08)09231-9
Keywords: Method of sub-supersolutions, Schauder's fixed point theorem, semilinear elliptic problems, weak solutions
Received by editor(s): September 12, 2006
Published electronically: February 29, 2008
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2008 American Mathematical Society