A new existence theory for periodic solutions to evolution equations. Issue 11 (17th August 2020)

• Record Type: Journal Article
• Authors: Ezzinbi, Khalil; Taoudi, Mohamed Aziz
• Is Part Of: Applicable analysis. Volume 99:Issue 11(2020)
• Page Start: 1939
• Page End: 1952
• Publication Date: 2020-08-17
• Subjects: Affine maps -- weak topology -- locally convex spaces -- fixed point theorems -- semigroups -- evolution equations -- functional differential equations; 47H10 -- 35B10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1551995
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: 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.