Boundedness of solutions of measure differential equations and dynamic equations on time scales. (English) Zbl 1369.34050
The authors study generalized ordinary differential equations in J. Kurzweil’s sense, and provide sufficient conditions ensuring that their solutions are uniformly bounded or uniformly ultimately bounded, respectively. These conditions require the existence of a Lyapunov functional with suitable properties.
The main results lead to corollaries dealing with uniform boundedness and uniform ultimate boundedness of solutions to measure differential equations and dynamic equations on time scales (it is known that both types of equations are special cases of generalized ordinary differential equations).
The main results lead to corollaries dealing with uniform boundedness and uniform ultimate boundedness of solutions to measure differential equations and dynamic equations on time scales (it is known that both types of equations are special cases of generalized ordinary differential equations).
Reviewer: Antonín Slavík (Praha)
MSC:
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34N05 | Dynamic equations on time scales or measure chains |
Keywords:
boundedness of solutions; generalized differential equations; measure differential equations; dynamic equations on time scales; Lyapunov functionalReferences:
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