New Almost Periodic Type Functions and Solutions of Differential Equations

Basit, Bolis ; Zhang, Chuanyi

Canadian journal of mathematics, Tome 48 (1996) no. 6, pp. 1138-1153

Résumé

Let X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from J to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.

Détail

DOI : 10.4153/CJM-1996-059-9

Mots-clés : 43A60, 28B05, 43A45, 34A12, 35K55, Recurrent, pseudo almost automorphic, asymptotically almost automorphic, indefinite integral, spectrum, parabolic partial equation

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