Description

• Title:
  Global structure of positive solutions for superlinear second order $m$-point boundary value problems
• Creator:
  Ma, Ruyun;
  An, Yulian
• Description:
  In this paper, we consider the nonlinear eigenvalue problems $$ \gather u''+\lambda h(t)f(u)=0, \quad 0< t< 1, \\ u(0)=0,\quad u(1)=\sum_{i=1}^{m-2}\alpha_iu(\eta_i), \endgather $$ where $m\geq 3$, $ \eta_i\in (0,1)$ and $\alpha_i> 0$ for $i=1,\ldots,m-2$, with $\sum_{i=1}^{m-2}\alpha_i\eta_i< 1$; $h\in C([0,1], [0,\infty))$ and $h(t)\ge 0$ for $t\in [0,1]$ and $h(t_0)> 0$ for $t_0\in [0,1]$; $f\in C([0,\infty),[0,\infty))$ and $f(s)> 0$ for $s> 0$, and $f_0=\infty$, where $f_0=\lim_{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using the nonlinear Krein-Rutman Theorem.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 34, No 2 (December 2009); 279 - 290;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.043/8621
• Subject:
  Multiplicity results;
  multi-point boundary value problem;
  eigenvalues;
  bifurcation methods;
  positive solutions;
  34B10;
  34G20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.043
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other