© 2019

Qualitative Analysis of Set-Valued Differential Equations


  • First book on the theoretical foundations of modeling real-world phenomena by a set of differential equations

  • Focusses on differential equations with uncertainty

  • Written for the experts working in the ?eld of qualitative analysis of di?erential and other types of equations


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Anatoly A. Martynyuk
    Pages 1-45
  3. Anatoly A. Martynyuk
    Pages 47-84
  4. Anatoly A. Martynyuk
    Pages 85-101
  5. Anatoly A. Martynyuk
    Pages 103-122
  6. Anatoly A. Martynyuk
    Pages 123-134
  7. Anatoly A. Martynyuk
    Pages 135-149
  8. Anatoly A. Martynyuk
    Pages 151-171
  9. Anatoly A. Martynyuk
    Pages 173-187
  10. Back Matter
    Pages 189-198

About this book


The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them.  The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness.

Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.


set equations regularization of uncertain set equations stability asymptotic stability boundedness mixed minkowski volumes

Authors and affiliations

  1. 1.Institute of MechanicsNational Academy of Sciences of UkraineKievUkraine

Bibliographic information