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Examples of the nonexistence of a solution in the presence of upper and lower solutions

Published online by Cambridge University Press:  17 February 2009

Patrick Habets  and
Rodrigo L. Pouso
Patrick Habets
Affiliation:
Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2, 1348 Louvain-La-Neuve, Belgium.
Rodrigo L. Pouso
Affiliation:
Dept. de Análise Matemática, Univ. de Santiago de Compostela, 15706 Santiago de Compostela, Spain; e-mail: [email protected].
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Abstract

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Standard results for boundary value problems involving second-order ordinary differential equations ensure that the existence of a well-ordered pair of lower and upper solutions together with a Nagumo condition imply existence of a solution. In this note we introduce some examples which show that existence is not guaranteed if no Nagumo condition is satisfied.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 4 , April 2003 , pp. 591 - 594
Copyright
Copyright © Australian Mathematical Society 2003

References

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