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Lyapunov inequalities for half-linear dynamic equations on time scales and disconjugacy. (English) Zbl 1211.26027

Summary: We establish a time scale version of the Lyapunov inequality for half-linear dynamic equations on time scales which provides the lower bound for the distance between consecutive zeros of solutions. Also, we establish some sufficient conditions for disconjugacy and study the asymptotic behavior of the oscillatory solutions. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of dynamic equations on time scales.

MSC:

26E70 Real analysis on time scales or measure chains
26D15 Inequalities for sums, series and integrals
26D20 Other analytical inequalities
39A12 Discrete version of topics in analysis
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