ANZIAM  J.  44 (2003), 591-594
Examples of the nonexistence of a solution in the presence of upper and lower solutions

Patrick Habets
  Institut de Mathématique Pure et Appliquée
  Chemin du Cyclotron, 2
  1348 Louvain-La-Neuve
Rodrigo L. Pouso
  Dept. de Análise Matemática
  Univ. de Santiago de Compostela
  15706 Santiago de Compostela

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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