Preface

Chapter 1 -
Linear and perturbed equations

Chapter 2 -
Nonlinear differential equations

Chapter 3 -
Semi-linear evolution equations

Chapter 4 -
Periodic solutions

Many real-life processes can be characterised by rapid changes in their state. Some of these changes begin impulsively and are not negligible. For changes such as these, mathematical models called non-instantaneous differential equations are created. These models give rise to a new, hybrid dynamical system that can be used for many different purposes.

Non-instantaneous impulsive differential equations are a useful tool to monitor the interjection of drugs and their consequential absorption into the bloodstream. They can also be widely used in physics, biology, dynamics and ecology, and have a far-ranging scope within the scientific industry.

This book is the result of four years of dedicated research and it provides a thorough exploration of the concepts and results of non-instantaneous differential equations. Existing material is explored, as well as the potential implications that these mathematical methods imply. Using a variety of equations, examples and solutions, this book will be an essential guide for researchers, graduate students and those interested in applied mathematics and related fields. It will also serve as a complimentary text for seminars and graduate courses.

JinRong Wang is a professor at Guizhou University in China and his expertise lies in numerical analysis, applied mathematics and differential equations. Michal Feckan is a professor at Comenius University in Bratislava and his research focuses on analysis and applied mathematics as well as numerical modelling and numerical analysis. Both authors of this book are known internationally for their expertise in both impulsive and non-instantaneous impulsive differential equations.