Description

• Title:
  Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type
• Creator:
  Webb, Jeffrey R. L.;
  Lan, Kunquan Q.
• Description:
  New criteria are established for the existence of multiple positive solutions of a Hammerstein integral equation of the form $$ u(t)= \int_{0}^1 k(t,s)g(s)f(s,u(s))ds \equiv Au(t) $$ where $k$ can have discontinuities in its second variable and $g \in L^{1}$. These criteria are determined by the relationship between the behaviour of $f(t,u)/u$ as $u$ tends to $0^+$ or $\infty$ and the principal (positive) eigenvalue of the linear Hammerstein integral operator $$ Lu(t)=\int_{0}^1 k(t,s)g(s)u(s)ds. $$ We obtain new results on the existence of multiple positive solutions of a second order differential equation of the form $$ u''(t)+g(t)f(t,u(t))=0 \quad\text{a.e. on } [0,1], $$ subject to general separated boundary conditions and also to nonlocal $m$-point boundary conditions. Our results are optimal in some cases. This work contains several new ideas, and gives a {\it unified} approach applicable to many BVPs.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2006.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 27, No 1 (March 2006); 91 - 115;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.003/8863
• Subject:
  Fixed point index;
  positive solution;
  eigenvalue criteria;
  Primary 34B18;
  Secondary 34B15;
  47H10;
  47H30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2006.003
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other