TY - JOUR
AU - M. S. Filipkovska
PY - 2018/06/25
Y2 - 2024/02/24
TI - Lagrange stability and instability of nonregular semilinear differential-algebraic equations and applications
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 6
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1598
AB - We consider an nonregular (singular) semilinear differential-algebraic equation $$\frac d{dt} [Ax] + Bx = f(t, x)$$ and prove thetheorems on Lagrange stability and instability. The theorems give sufficient conditions for the existence, uniqueness, andboundedness of a global solution of the Cauchy problem for the semilinear differential-algebraic equation and sufficientconditions 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 tothe global Lipschitz condition. This enables us to use them for solving more general classes of applied problems. Twomathematical models of radioengineering filters with nonlinear elements are studied as applications.
ER -