Viability, Invariance and Applications

The book is an almost self-contained presentation of the important concepts and results in viability and invariance. The viability of a set K in the differential equation (or inclusion) driven by that or multi-function function) to have at least one solution. The invariance of a set A set of functions (or multi-function) F, a form of a larger set in K, at least for a short time.

The Naguo's Viability Theorem for ordinary differential equations with continuing right-hand or continuous nonlinear evolution equations, systems and inclusions . In the latter (ie, multi-valued) cases, the results (based on three completely new concepts), are all well-known, classical and counterparts.

- New concepts for multi-functions as the classical tangent vectors for functions
- Provides the very eventual and non-linear conditions in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions
- Clarifying examples, illustrations and numerous problems, completely and carefully solved
- Illustrates the applications from theory into practice
- Very clear and elegant style

Preface
Chapter 1. Generalities
Chapter 2. Specific preliminary results
Ordinary differential equations and inclusions
Chapter 3. Nagumo type viability theorems
Chapter 4. Problems of invariance
Chapter 5. Viability under Carathéodory conditions
Chapter 6. Viability for differential inclusions
Chapter 7. Applications
Part 2 Evolution equations and inclusions
Chapter 8. Viability for single-valued semilinear evolutions
Chapter 9. Viability for multi-valued semilinear evolutions
Chapter 10. Viability for single-valued fully nonlinear evolutions
Chapter 11. Viability for multi-valued fully nonlinear evolutions
Chapter 12. Carathéodory perturbations of m-dissipative operators
Chapter 13. Applications
Solutions to the proposed problems
Bibliographical notes and comments
Bibliography
Name Index
Subject Index
Notation