It is the purpose of this paper to give oscillation criteria for the third order nonlinear delay dynamic equation on a time scale T, where ฮณ โฅ 1 is the quotient of odd positive integers, a and r are positive rd-continuous functions on T, and the so-called delay function ฯ : T โ T satisfies ฯ (t) โค
Asymptotic behavior of solutions of third-order nonlinear dynamic equations on time scales
โ Scribed by Zhi-Hua Yu; Qi-Ru Wang
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 586 KB
- Volume
- 225
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
โฆ Synopsis
a b s t r a c t
In this paper, we will study asymptotic behavior of solutions to third-order nonlinear dynamic equations on time scales of the form 1
By using the Riccati technique and integral averaging technique, two different types of criteria are established, one of which extends some existing results and the other is new. Two examples of dynamic equations on different time scales are given to show the applications of the obtained results.
๐ SIMILAR VOLUMES
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Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and the Young inequality. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.
Consider the third-order nonlinear differential equation We obtain sufficient conditions for every solution of the equation to be bounded; we also establish criteria for every solution of the equation to converge to zero.