A new existence theory for periodic solutions to evolution equations

This paper deals with a new existence theory for periodic solutions to a broad class of evolution equations. We first establish new fixed point theorems for affine maps in locally convex spaces and ordered Banach spaces. Our new fixed point results extend, encompass and complement a number of well-k...

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Bibliographic Details
Published inApplicable analysis Vol. 99; no. 11; pp. 1939 - 1952
Main Authors Ezzinbi, Khalil, Taoudi, Mohamed Aziz
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 17.08.2020
Taylor & Francis Ltd
Subjects
Affine maps
Banach spaces
Evolution
evolution equations
Existence theorems
fixed point theorems
Fixed points (mathematics)
functional differential equations
Linear systems
locally convex spaces
Mathematical analysis
semigroups
weak topology
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Summary:This paper deals with a new existence theory for periodic solutions to a broad class of evolution equations. We first establish new fixed point theorems for affine maps in locally convex spaces and ordered Banach spaces. Our new fixed point results extend, encompass and complement a number of well-known theorems in the literature, including the famous Chow and Hale fixed point theorem. With these obtained fixed point results, we investigate the existence of periodic solutions for some class of nonhomogeneous linear systems in Banach spaces with lack of compactness. Some illustrative examples are also given.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2018.1551995