@article{Filipkovska_2018, title={Lagrange stability and instability of nonregular semilinear differential-algebraic equations and applications}, volume={70}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1598}, abstractNote={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 problem for the semilinear differential-algebraic equation and sufficient
conditions for the existence and uniqueness of the solution with finite escape time for the analyzed Cauchy problem
(this solution is defined on a finite interval and unbounded). The proposed theorems do not contain constraints similar to
the global Lipschitz condition. This enables us to use them for solving more general classes of applied problems. Two
mathematical models of radioengineering filters with nonlinear elements are studied as applications.}, number={6}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Filipkovska, M. S.}, year={2018}, month={Jun.}, pages={823-847} }