Generalizations of Krasnosel'skiĭ's fixed point theorem in cones and applications
type: Item
instance of: scholarly article
title: Generalizations of Krasnosel'skiĭ's fixed point theorem in cones and applications
zbMATH Open document ID: 1422.47057
author: Sorin Budisan
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-04-04T00:00:00Z
review text: The author proves several fixed point results for completely continuous maps on cones in Banach spaces in the spirit of \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673--688 (1979; Zbl 0421.47033)] \{the page numbers for this item are missing in the bibliography\}. The details are (to put it mildly) somewhat technical. In addition, the author proves the existence of a positive solution to the boundary problem \(u''(t)+f(t,u(t))=0\) on \([0,1]\) with zero boundary conditions with a non-negative continuous right hand side \(f:[0,1]\times\mathbb{R}_+\to\mathbb{R}_+\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47H07
zbMATH DE Number: 6700740
zbMATH Keywords: fixed point
zbMATH Keywords: cone
zbMATH Keywords: boundary value problem
reviewed by: Christian Fenske
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6700740