On the oscillation of certain second order nonlinear dynamic equations
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...
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th-mahidol.274972018-09-13T13:47:53Z On the oscillation of certain second order nonlinear dynamic equations Said R. Grace Ravi P. Agarwal Billûr Kaymakçalan Wichuta Sae-jie Cairo University, Faculty of Engineering Florida Institute of Technology Georgia Southern University Mahidol University Computer Science Mathematics 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. 2018-09-13T06:34:18Z 2018-09-13T06:34:18Z 2009-07-01 Article Mathematical and Computer Modelling. Vol.50, No.1-2 (2009), 273-286 10.1016/j.mcm.2008.12.007 08957177 2-s2.0-67349216027 https://repository.li.mahidol.ac.th/handle/123456789/27497 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=67349216027&origin=inward |
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Computer Science Mathematics Said R. Grace Ravi P. Agarwal Billûr Kaymakçalan Wichuta Sae-jie On the oscillation of certain second order nonlinear dynamic equations |
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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. |
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Cairo University, Faculty of Engineering |
| author_facet |
Cairo University, Faculty of Engineering Said R. Grace Ravi P. Agarwal Billûr Kaymakçalan Wichuta Sae-jie |
| format |
Article |
| author |
Said R. Grace Ravi P. Agarwal Billûr Kaymakçalan Wichuta Sae-jie |
| author_sort |
Said R. Grace |
| title |
On the oscillation of certain second order nonlinear dynamic equations |
| title_short |
On the oscillation of certain second order nonlinear dynamic equations |
| title_full |
On the oscillation of certain second order nonlinear dynamic equations |
| title_fullStr |
On the oscillation of certain second order nonlinear dynamic equations |
| title_full_unstemmed |
On the oscillation of certain second order nonlinear dynamic equations |
| title_sort |
on the oscillation of certain second order nonlinear dynamic equations |
| publishDate |
2018 |
| url |
https://repository.li.mahidol.ac.th/handle/123456789/27497 |
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1763495044221763584 |