Instability of set differential equations

Slyn'ko, V.; TUNÇ, Cemil

doi:10.1016/j.jmaa.2018.07.048

Instability of set differential equations

Atıf İçin Kopyala

Slyn'ko V. I., TUNÇ C.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.467, sa.2, ss.935-947, 2018 (SCI-Expanded)

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.