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

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Habets, Patrick [UCL] Pouso, RL

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2003
Language Anglais
Journal information "The A N Z I A M Journal" - Vol. 44, p. 591-594 (2003)
Peer reviewed yes
Publisher Australian Mathematics Publ Assoc Inc (Canberra)
issn 1446-1811
e-issn 1446-8735
Publication status Publié
Affiliation UCL - FSA/INMA - Département d'ingénierie mathématique
Links
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  6. Picard, J. de Math., 9, 217 (1893)
  7. Piccinini, Ordinary differential equations in, 39 (1984)
  8. Rouche, Equations différentielles ordinaires (1973)
  9. Scorza Dragoni, Giornale di Mat. (Battaglini), 69, 77 (1931)
  10. Scorza Dragoni, Rend. Semin. R. Accad. Naz. Lincei, 28, 317 (1938)
Bibliographic reference Habets, Patrick ; Pouso, RL. Examples of the nonexistence of a solution in the presence of upper and lower solutions. In: The A N Z I A M Journal, Vol. 44, p. 591-594 (2003)
Permanent URL http://hdl.handle.net/2078.1/41059