Multiple positive solutions for a class of nonlinear integro-differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Multiple positive solutions for a class of nonlinear integro-differential equations in Banach spaces
zbMATH Open document ID: 1064.45011
DOI: 10.1016/S0096-3003(03)00728-8
author: Dajun Guo
published in: Applied Mathematics and Computation
publication date: 2004-10-01T00:00:00Z
review text: The author investigates the boundary value problem (BVP) of mixed type described by \[ \begin{gathered} -u^{(n)}(t)= f(t, u(t), u'(t),\dots, u^{(n-1)}(t), (Tu)(t), (Su)(t))\;\forall t\in J,\\ u^{(i)}(0)= \theta\,(i= 0,1,\dots, n-2),\quad u^{(n-1)}(\infty)= \theta\end{gathered} \] with \(J = [0,\infty)\), and \(f\) continuous in all its arguments on \(J\times P\times P\times\cdots\times P\), \(P\), where \(P\) stands for a cone in a real Banach space \(E\), while \[ (Tu)(t)= \int^t_0 K(t, s)u(s)\,ds,\quad (Su)(t)= \int^\infty_0 H(t,s) u(s)\,ds. \] After proving three auxuliary lemmas, the author states and proves two existence theorems for the above formulated BVP. The hypotheses are rather technical and cannot be reproduced here. The method of subsolutions and supersolutions is used. Fixed point theorems provide the tools.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 2105567
zbMATH Keywords: higher-order integro-differential equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: Banach space
zbMATH Keywords: method of subsolutions and supersolutions
zbMATH Keywords: nonlinear integro-differential equations
reviewed by: Constantin Corduneanu
MaRDI profile type: Publication
cites work: A boundary value problem for \(n\)th order integro-differential equations in a Banach space
cites work: Minimal nonnegative solutions for \(n\)th order integro-differential equations in Banach spaces
cites work: Existence of solutions for \(n\)th-order integro-differential equations in Banach spaces
cites work: Q3994493
cites work: Q4716265
description: scientific article; zbMATH DE number 2105567