Description

• Title:
  A three critical points theorem and its applications to the ordinary Dirichlet problem
• Creator:
  Averna, Diego;
  Bonanno, Gabriele
• Description:
  The aim of this paper is twofold. On one hand we establish a three critical points theorem for functionals depending on a real parameter $\lambda \in \Lambda$, which is different from the one proved by B. Ricceri in [Arch. Math. {\bf 75} (2000), 220-226] and gives an estimate of where $\Lambda$ can be located. On the other hand, as an application of the previous result, we prove an existence theorem of three classical solutions for a two-point boundary value problem which is independent from the one by J. Henderson and H. B. Thompson [J. Differential Equations {\bf 166} (2000), 443-454]. Specifically, an example is given where the key assumption of [J. Differential Equations {\bf 166} (2000), 443-454] fails. Nevertheless, the existence of three solutions can still be deduced using our theorem.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 22, No 1 (September 2003); 93 - 103;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.029/9591
• Subject:
  Critical points;
  three solutions;
  two point boundary value problem;
  58E05;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.029
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other