Instability of set differential equations


Slyn'ko V. I. , TUNÇ C.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.467, ss.935-947, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 467 Konu: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jmaa.2018.07.048
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.935-947

Özet

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.