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Initial time difference stability in terms of two measures and a variational comparison result. (English) Zbl 1149.34034

This paper investigates initial time difference stability in terms of two measures and generalized variation of parameter techniques are unified with Lyapunov-like functions to establish a variational comparison result. At the beginning, the definitions necessary for the analysis of the initial time difference stability in terms of two measures are given. Further, a variational comparison result for vector Lyapunov-like functions is presented and applied to establish an initial time difference stability criteria in terms of two measures. An example is presented to illustrate how the results can be applied.

MSC:

34D23 Global stability of solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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