A new existence theory for periodic solutions to evolution equations |
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Authors: | Khalil Ezzinbi |
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Institution: | Faculté des Sciences Semlalia, Département de Mathématiques, Université Cadi Ayyad, Marrakesh, Morocco |
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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. |
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Keywords: | Affine maps weak topology locally convex spaces fixed point theorems semigroups evolution equations functional differential equations |
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