Global boundedness and stability of solutions of nonautonomous degenerate differential equations. (English) Zbl 1461.34018
Summary: For nonautonomous (time-varying) degenerate differential equations, which are also called nonautonomous differential-algebraic equations, conditions of the Lagrange stability and instability, the Lyapunov stability and instability, ultimate boundedness and asymptotic stability, including conditions of asymptotic stability in the large (or complete stability) are obtained. Note that the Lagrange stability of the equation (as well as the ultimate boundedness) guarantees its global solvability for all consistent initial values and the boundedness (the ultimate boundedness) of all its solutions. The Lagrange instability enable to identify solutions with a finite escape time, i.e., the solutions blowing up in finite time.
MSC:
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
Keywords:
nonautonomous; global boundedness of solutions; Lagrange stability; ultimate boundedness; Lyapunov stability; asymptotic stability in the large; degenerate differential equation; differential-algebraic equationReferences:
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