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Boundedness and exponential stability of solutions to dynamic equations on time scales. (English) Zbl 1118.34030
Summary: Using the generalized time scales exponential function, we give a new definition for the exponential stability of solutions for dynamic equations on time scales. Employing Lyapunov-type functions on time scales, we investigate the boundedness and the exponential stability of solutions to first-order dynamic equations on time scales, and some sufficient conditions are obtained. Some examples are given at the end of this paper.
MSC:
34C11Qualitative theory of solutions of ODE: growth, boundedness
34D20Stability of ODE
39A10Additive difference equations