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

 

Fredholm alternative and boundary value problems


Author: Stanis{l}aw Sedziwy
Journal: Proc. Amer. Math. Soc. 132 (2004), 1779-1784
MSC (2000): Primary 34B15
Published electronically: November 4, 2003
MathSciNet review: 2051141
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Abstract: This note presents a simple proof of A. Lasota's application of the nonlinear Fredholm alternative to the existence proofs of the boundary value problems involving ordinary differential equations. It then uses Lasota's result to get a stronger version of the theorem of Herzog and Lemmert on the Dirichlet boundary value problem for the second-order systems of ordinary differential equations.


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Additional Information

Stanis{l}aw Sedziwy
Affiliation: Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30-072 Cracow, Poland
Email: sedziwy@softlab.ii.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07256-3
PII: S 0002-9939(03)07256-3
Keywords: Boundary value problem, Fredholm alternative, Homogeneous map
Received by editor(s): November 5, 2002
Received by editor(s) in revised form: February 17, 2003
Published electronically: November 4, 2003
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society