ANZIAM J.
44 (2003), 591-594
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Examples of the nonexistence of a solution in the presence of upper and lower solutions
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Patrick Habets
Institut de Mathématique Pure et Appliquée
Chemin du Cyclotron, 2
1348 Louvain-La-Neuve
Belgium
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Rodrigo L. Pouso
Dept. de Análise Matemática
Univ. de Santiago de Compostela
15706 Santiago de Compostela
Spain
rodrigolp@usc.es
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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.
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