Fixed point index and solutions of differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Fixed point index and solutions of differential equations in Banach spaces
zbMATH Open document ID: 1078.47020
author: Zhi-Qin Han
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2005-04-26T00:00:00Z
review text: In reflexive Banach spaces by constructing homotopies, the author presents a formula for the computation of the fixed point index for completely continuous operators by the solutions of the corresponding ordinary differential equations. The main result is the following: Assume that \(\Omega\subset X\) is open bounded, \(A: P\to P\) is completely continuous, locally Lipschitzian and \(Ax\neq x\) for every \(x\in \partial\Omega\cap P.\) Then \(i(A,\Omega\cap P,P)=\lim_{t\to 0+}i(S(t),\Omega\cap P,P).\) The formula is then used to obtain fixed points for completely continuous operators on cones.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 2161541
zbMATH Keywords: fixed point index
zbMATH Keywords: completely continuous operators
zbMATH Keywords: strict \(k\)-set contraction
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161541