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

• Autores: Patrick Habets , Rodrigo López Pouso
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 44, Nº 4, 2003, págs. 591-594
• Idioma: inglés
• DOI: 10.1017/s1446181100012955
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• Resumen

  • 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.