Saker, S. H. Lyapunov inequalities for half-linear dynamic equations on time scales and disconjugacy. (English) Zbl 1211.26027 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 18, No. 2, 149-161 (2011). 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. Cited in 6 Documents 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 Keywords:dynamic equations; time scale; Lyapunov inequality PDFBibTeX XMLCite \textit{S. H. Saker}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 18, No. 2, 149--161 (2011; Zbl 1211.26027)