Pseudo almost periodic functions in Banach spaces. (English) Zbl 1234.43002

Diagana, Toka

New York, NY: Nova Science Publishers (ISBN 978-1-60021-637-4). xiv, 132 p. (2007).

Publisher’s description: This book provides the reader with a comprehensive and accessible introduction to the concepts of almost periodicity and pseudo almost periodicity as well as their applications to differential equations, partial differential equations, integral equations, and partial neutral functional differential equations with delay on Banach spaces. Further, the book offers various suffcient conditions, which do guarantee the existence and uniqueness of (pseudo) almost periodic solutions to the heat equation, reaction-diffusion equation, transport equation, logistic equation with delay, and neutral partial functional differential equations with delays arising in control systems. To obtain those existence results, the author makes use of various techniques such as semigroup methods combined with some classical fixed-point theorems, the so-called method of the invariant subspaces for unbounded linear operators, Zima’s fixed-point theorem, and many more.

MSC:

43A60	Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations
34K30	Functional-differential equations in abstract spaces
35B15	Almost and pseudo-almost periodic solutions to PDEs
46C05	Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47D06	One-parameter semigroups and linear evolution equations
47E05	General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)