Semilinear evolution equations and their applications. (English) Zbl 1414.34002

Diagana, Toka

Cham: Springer (ISBN 978-3-030-00448-4/hbk; 978-3-030-00449-1/ebook). xx, 189 p. (2018).

This book is, in a sense, the continuation of the author’s monograph [Almost automorphic type and almost periodic type functions in abstract spaces. Cham: Springer (2013; Zbl 1279.43010)] and presents results on: Nonautonomous difference equations (Ch. 5), Singular difference equations (Ch. 6), Fractional integro-differential equations (Ch. 7), First-order semilinear evolution equations (Ch. 8), Semilinear fractional evolution equations (Ch. 9), Second-order semilinear evolution equations (Ch. 10). These are preceded by the introductory material on: Banach and Hilbert spaces (Ch. 1), Operator theory (Ch. 2), Semi-group of linear operators (Ch. 3), Almost periodic functions and sequences (Ch. 4). Applications to partial differential equations and dynamics of population models are also discussed.

Reviewer: Piotr Biler (Wrocław)

MSC:

34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations
34K14	Almost and pseudo-almost periodic solutions to functional-differential equations
39-02	Research exposition (monographs, survey articles) pertaining to difference and functional equations
34G20	Nonlinear differential equations in abstract spaces
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
34A08	Fractional ordinary differential equations
45Jxx	Integro-ordinary differential equations

Keywords:

difference equation; fractional integro-differential equation; semilinear evolution equation

Citations:

Zbl 1279.43010