Lagrange stability and instability of nonregular semilinear differential-algebraic equations and applications

• Date: 2018
• Main Authors: Filipkovska, M. S., Филипковская, М. С.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1598
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider an nonregular (singular) semilinear differential-algebraic equation $$\frac d{dt} [Ax] + Bx = f(t, x)$$ and prove the theorems on Lagrange stability and instability. The theorems give sufficient conditions for the existence, uniqueness, and boundedness of a global solution of the Cauchy...