Instability of set differential equations
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.467, sa.2, ss.935-947, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 467 Sayı: 2
- Basım Tarihi: 2018
- Doi Numarası: 10.1016/j.jmaa.2018.07.048
- Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.935-947
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
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.