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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Semilinear elliptic equations and fixed points


Author: Cleon S. Barroso
Journal: Proc. Amer. Math. Soc. 133 (2005), 745-749
MSC (2000): Primary 35J25; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-04-07718-4
Published electronically: October 21, 2004
MathSciNet review: 2113923
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Abstract: In this paper, we deal with a class of semilinear elliptic equations in a bounded domain $\Omega\subset\mathbb{R} ^N$, $N\geq 3$, with $C^{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.


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Additional Information

Cleon S. Barroso
Affiliation: Departamento de Matematica, Universidade Federal do Ceará, Campus do Pici, Bl. 914, Fortaleza-Ce, 60455-760, Brazil
Email: cleonbar@mat.ufc.br

DOI: https://doi.org/10.1090/S0002-9939-04-07718-4
Keywords: Semilinear elliptic equations, fixed point theorem, Krasnoselskii
Received by editor(s): September 25, 2003
Published electronically: October 21, 2004
Additional Notes: This research was supported by Capes, Brazil
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2004 American Mathematical Society