Instability of set differential equations


Slyn'ko V. I. , TUNÇ C.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.467, no.2, pp.935-947, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 467 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jmaa.2018.07.048
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.935-947

Abstract

This paper is devoted to the instability of Set Differential Equations (SDEs). Using the geometric inequalities of Brunn-Minkowski and A.D. Aleksandrov, we propose new methods for constructing Lyapunov functions. In combination with the known methods of stability theory, the Lyapunov's direct method, the comparison method and the vector-function method, we establish conditions for the collapse of the solutions of the SDEs. Estimates of the collapse time of solutions are also obtained. Examples of SDEs in spaces of dimension 2 and 3 illustrating general theorems are given. (C) 2018 Published by Elsevier Inc.