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Boundedness and uniqueness of solutions to dynamic equations on time scales. (English) Zbl 1072.39017

The authors investigate the boundedness and uniqueness of solutions to systems of dynamical equations in the more general time scale setting. They give some basic definitions for the dynamical equations

x Δ =f(t,x),t0(1)
x(t 0 )=x 0 ,t 0 x 0 ·(2)

They define suitable Lyapunov-type functions on time scales and then formulate appropriate inequalities on these functions that guarantee solutions to (1) and (2) are uniformly bounded and unique. These results are generalizations of known results for the case T=. Some results on the boundedness of solutions of equations (1) and (2) are deduced with examples. The uniqueness of the solutions is also represented.

MSC:
39A12Discrete version of topics in analysis
39A11Stability of difference equations (MSC2000)
34A34Nonlinear ODE and systems, general