Advanced Functional Evolution Equations and Inclusions

ISBN-13: 9783319177670 / Angielski / Twarda / 2015 / 408 str.

Mouffak Benchohra; Said Abbas

Opis

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Frechet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks.This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Recenzje

"In this monograph, the authors present their results on various partial functional and neutral functional differential equations and inclusions in infinite dimensional spaces obtained in the last years. The book is organized in 13 chapters, an extensive bibliography and an index. ... This book will be useful to researchers and graduate students interested in functional evolution equations and inclusions." (Rodica Luca, zbMATH, Vol. 1326.34012, 2016)

Spis treści

1. Preliminary Background.- 2. Partial Functional Evolution Equations with Finite Delay.- 3. Partial Functional Evolution Equations with Infinite Delay.- 4. Perturbed Partial Functional Evolution Equations.- 5. Partial Functional Evolution Inclusions with Finite Delay.- 6. Partial Functional Evolution Inclusions with Infinite Delay.- 7. Densely Defined Functional Differential Inclusions with Finite Delay.- 8. Non-Densely Defined Functional Differential Inclusions with Finite Delay.- 9. Impulsive Semi-linear Functional Differential Equations.- 10. Impulsive Functional Differential Inclusions with Unbounded Delay.- 11. Functional Differential Inclusions with Multi-valued Jumps.- 12. Global Existence Results for Functional Differential Equations and Inclusions with Delay.- 13. Global Existence Results of Second Order Functional Differential Equations with Delay.- References.- Index.

Blurb

​This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks.

This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.