Publication: On the oscillation of certain second order nonlinear dynamic equations
Issued Date
2009-07-01
Resource Type
ISSN
08957177
Other identifier(s)
2-s2.0-67349216027
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Mahidol University
Rights Holder(s)
SCOPUS
Bibliographic Citation
Mathematical and Computer Modelling. Vol.50, No.1-2 (2009), 273-286
Suggested Citation
Said R. Grace, Ravi P. Agarwal, Billûr Kaymakçalan, Wichuta Sae-jie On the oscillation of certain second order nonlinear dynamic equations. Mathematical and Computer Modelling. Vol.50, No.1-2 (2009), 273-286. doi:10.1016/j.mcm.2008.12.007 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/27497
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Title
On the oscillation of certain second order nonlinear dynamic equations
Abstract
We establish some new oscillation criteria for solutions to the second order nonlinear dynamic equation (a (xΔ)α)Δ (t) + q (t) xβ (t) = 0 on an arbitrary time scale T, where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on T. The results are obtained when ∫∞ a- 1 / α (s) Δ s < ∞ or ∫∞ a- 1 / α (s) Δ s = ∞. These criteria unify and extend known results for the corresponding half-linear and nonlinear differential and difference equations. Some of our results are new even in the continuous and discrete cases. © 2009 Elsevier Ltd. All rights reserved.