Multiple positive solutions for first order nonlinear integro-differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Multiple positive solutions for first order nonlinear integro-differential equations in Banach spaces
zbMATH Open document ID: 1026.45013
DOI: 10.1016/S0362-546X(02)00165-7
author: Dajun Guo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-28T00:00:00Z
review text: Using the fixed point index theory some results on the existence of multiple positive solutions of the following problem are obtained: \[ (1)\quad u'(t)= f\bigl(t,u(t), (Tu)(t),(Su)(t)\bigr),\;t\in\mathbb{R}_+,\qquad (2)\quad u (\infty) =\beta u(0). \] The problem (1)--(2) is considered in a real Banach space \(E\) with a normal solid cone \(P\) defining a partial ordering in \(E\). It is assumed that \(f\in C(\mathbb{R}_+\times P\times P\times P,P)\), \(\beta>1\) and \[ (Tu)(t)=\int^t_0 k(t,s)u(s)ds, \quad(Su)(t)=\int^\infty_0 H(t,s)u(s)ds. \] Apart from this some additional conditions are assumed. The obtained results are illustrated by two interesting examples.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1902842
zbMATH Keywords: integro-differential equation
zbMATH Keywords: multiple positive solutions
zbMATH Keywords: ordered Banach space
zbMATH Keywords: fixed point index
zbMATH Keywords: normal solid cone
reviewed by: Józef Banaś
MaRDI profile type: Publication
cites work: Combined effects of concave and convex nonlinearities in some elliptic problems
cites work: Q3883053
cites work: Multiple positive solutions of impulsive nonlinear Fredholm integral equations and applications
cites work: Second order integro-differential equations of Volterra type on unbounded domains in Banach spaces
cites work: Minimal nonnegative solutions for \(n\)th order integro-differential equations in Banach spaces
cites work: Q3994493
cites work: Q4716265
cites work: On multiple positive solutions of nonlinear elliptic eigenvalue problems
cites work: Multiplicity Results for Two Classes of Boundary-Value Problems
description: scientific article; zbMATH DE number 1902842