Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems

Sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions. The conditions assume the existence of a strong upper solution–lower solution pair, a concept that is defined in the paper. The differential equation...

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Bibliographic Details
Published in:Journal of Differential Equations 2002-03, Vol.180 (1), p.51-64
Main Authors: Ehme, Jeffrey, Eloe, Paul W., Henderson, Johnny
Format: Article
Language:English
Subjects:
Nagumo condition
nonlinear boundary value problems
upper and lower solution
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Summary:Sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions. The conditions assume the existence of a strong upper solution–lower solution pair, a concept that is defined in the paper. The differential equation has nonlinear dependence on all lower order derivatives of the unknown; in particular, appropriate Nagumo conditions are obtained and employed.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.2001.4056