Periodic solutions of non-densely defined delay evolution equations
type: Item
instance of: scholarly article
title: Periodic solutions of non-densely defined delay evolution equations
zbMATH Open document ID: 1018.34063
DOI: 10.1155/S1048953302000114
author: J. Liu
author: Khalil Ezzinbi
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2003-09-11T00:00:00Z
review text: Summary: The authors study the finite delay evolution equation \[ x'(t)= Ax(t)+ F(t,x_t),\quad t\geq 0,\quad x_0= \varphi\in C([-r,0],E), \] where the linear operator \(A\) is nondensely defined and satisfies the Hille-Yosida condition. First, they obtain some properties of ``integral solutions'' for this case and prove the compactness of an operator determined by integral solutions. This allows them to apply Horn's fixed-point theorem to prove the existence of periodic integral solutions when integral solutions are bounded and ultimately bounded. This extends the study of periodic solutions for densely operators to the nondensely defined operators. An example is given.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1844034
zbMATH Keywords: periodic solutions
zbMATH Keywords: finite delay evolution equation
zbMATH Keywords: existence
zbMATH Keywords: integral solutions
MaRDI profile type: Publication
Recommended article: Periodic solutions of non-densely non-autonomous differential equations with delay
Recommended article: Periodic solutions to non-autonomous evolution equations with multi-delays
Recommended article: Periodic solutions for a class of non-autonomous differential delay equations
Recommended article: Periodic solutions of infinite delay evolution equations
Recommended article: Periodic solutions of differential equations with delay depending on solution
Recommended article: Q3123363
Recommended article: Q3595166
Recommended article: Periodic solutions for equations with distributed delays
Recommended article: Q3573745
Recommended article: Q5435754
description: scientific article; zbMATH DE number 1844034