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June 2017 Opial and Lyapunov inequalities on time scales and their applications to dynamic equations
Nguyen Du Vi Nhan, Tran Dinh Phung, Dinh Thanh Duc, Vu Kim Tuan
Kodai Math. J. 40(2): 254-277 (June 2017). DOI: 10.2996/kmj/1499846597

Abstract

We prove some weighted inequalities for delta derivatives acting on products and compositions of functions on time scales and apply them to obtain generalized dynamic Opial-type inequalities. We also employ these inequalities to establish some new dynamic Lyapunov-type inequalities, which are essential in studying disfocality, disconjugacy, lower bounds of eigenvalues, and distance between generalized zeros for half-linear dynamic equations. In particular, we solve an open problem posed by Saker in [Math. Comput. Modelling 58 (2013), 1777-1790]. Moreover, the results presented in this paper generalize, improve, extend, and unify most of known results not only in the discrete and continuous analysis but also on time scales.

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Nguyen Du Vi Nhan. Tran Dinh Phung. Dinh Thanh Duc. Vu Kim Tuan. "Opial and Lyapunov inequalities on time scales and their applications to dynamic equations." Kodai Math. J. 40 (2) 254 - 277, June 2017. https://doi.org/10.2996/kmj/1499846597

Information

Published: June 2017
First available in Project Euclid: 12 July 2017

zbMATH: 1380.26016
MathSciNet: MR3680561
Digital Object Identifier: 10.2996/kmj/1499846597

Rights: Copyright © 2017 Tokyo Institute of Technology, Department of Mathematics

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Vol.40 • No. 2 • June 2017
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