Description

• Title:
  Nontrivial solutions of fourth-order singular boundary value problems with sign-changing nonlinear terms
• Creator:
  Zhang, Kemei
• Description:
  In this paper, the fourth-order singular boundary value problem (BVP) $$ \aligned &u^{(4)}(t)=h(t)f(u(t)),\ \ t\in(0,1),\\ &u(0)=u(1)=u'(0)=u'(1)=0\endaligned $$ is considered under some conditions concerning the first characteristic value corresponding to the relevant linear operator, where $h$ is allowed to be singular at both $t=0$ and $t=1$. In particular, $f\colon (-\infty,\infty)\rightarrow (-\infty,\infty)$ may be a sign-changing and unbounded function from below, and it is not also necessary to exist a control function for $f$ from below. The existence results of nontrivial solutions and positive-negative solutions are given by the topological degree theory and the fixed point index theory, respectively.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 40, No 1 (September 2012); 53 - 70;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.022/8371
• Subject:
  Nontrivial solution;
  topological degree;
  fixed point index;
  55M20;
  55M25;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.022
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other