Almost Periodic Solutions of Impulsive Differential Equations

ISBN-13: 9783642275456 / Angielski / Miękka / 2012 / 217 str.

Gani T. Stamov

Opis

In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.

Recenzje

From the reviews:

"The aim of this book is to study quantitatively and qualitatively impulsive differential equations in finite- and/or infinite-dimensional spaces. ... This book is very important for researchers who work on differential equations with piecewise dynamics. The book is well written and each chapter is self-contained. It presents many results and gives satisfactory answers to many open problems posed in the field." (Khalil Ezzinbi, Mathematical Reviews, January, 2013)

"The author presents a general description of impulsive differential equations, existence and uniqueness, piecewise continuous Lyapunov functions, almost periodic sequences and almost periodic functions. ... This interesting monograph written by a known specialist in the field is addressed to a wide audience, not only mathematicians, but also engineers, biologists and physicists." (Addelghani Ouahab, Zentralblatt MATH, Vol. 1255, 2013)

Spis treści

1 Impulsive Differential Equations and Almost Periodicity.- 2 Almost Periodic Solutions.- 3 Lyapunov Method and Almost Periodicity.- 4 Applications.

Blurb

Impulsive differential equations are suitable for the mathematical simulation of evolutionary processes in which the parameters undergo relatively long periods of smooth variation followed by short-term rapid changes (that is, jumps) in their values. Processes of this type are often investigated in various fields of science and technology. The question of the existence and uniqueness of almost periodic solutions of differential equations is an age-old problem of great importance. The qualitative theory of impulsive differential equations is currently undergoing rapid development in relation to the investigation of various processes which are subject to impacts during their evolution, and many findings on the existence and uniqueness of almost periodic solutions of these equations are being made.
This book systematically presents findings related to almost periodic solutions of impulsive differential equations and illustrates their potential applications.