The existence of bounded solutions of a degenerate linear nonhomogeneous impulsive system. (Ukrainian. English summary) Zbl 1363.34035
Summary: We consider a degenerate system which can be reduced to the central canonical form and such that the corresponding homogeneous nondegenerate system is exponentially dichotomous on the semi-axes. We obtain a necessary and sufficient condition for the existence and uniqueness of a solution bounded on the whole axis of the degenerate system of differential equations with impulse action at fixed points of time.
MSC:
34A30 | Linear ordinary differential equations and systems |
34A37 | Ordinary differential equations with impulses |
34D09 | Dichotomy, trichotomy of solutions to ordinary differential equations |
34C11 | Growth and boundedness of solutions to ordinary differential equations |