A new existence theory for periodic solutions to evolution equations

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.

Keywords:

• Affine maps
• weak topology
• locally convex spaces
• fixed point theorems
• semigroups
• evolution equations
• functional differential equations

AMS Subject Classifications:

• 47H10
• 35B10

Disclosure statement

No potential conflict of interest was reported by the authors.