OSCILLATORY AND ASYMPTOTIC CRITERIA OF THIRD ORDER NONLINEAR DELAY DYNAMIC EQUATIONS WITH DAMPING TERM ON TIME SCALES

Qinghua Feng

doi:10.11948/2018.1260

2018 Volume 8 Issue 4

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Qinghua Feng. OSCILLATORY AND ASYMPTOTIC CRITERIA OF THIRD ORDER NONLINEAR DELAY DYNAMIC EQUATIONS WITH DAMPING TERM ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1260-1281. doi: 10.11948/2018.1260

Citation:

Qinghua Feng. OSCILLATORY AND ASYMPTOTIC CRITERIA OF THIRD ORDER NONLINEAR DELAY DYNAMIC EQUATIONS WITH DAMPING TERM ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2018, 8(4): 1260-1281. doi: 10.11948/2018.1260

OSCILLATORY AND ASYMPTOTIC CRITERIA OF THIRD ORDER NONLINEAR DELAY DYNAMIC EQUATIONS WITH DAMPING TERM ON TIME SCALES

Qinghua Feng

School of Mathematics and Statistics, Shandong University of Technology, Zhangzhou Road 12, 255049, Zibo, China

Fund Project:

Abstract

Abstract

In this paper, we are concerned with oscillatory and asymptotic behavior of third order nonlinear delay dynamic equations with damping term on time scales. By using a generalized Riccati function and inequality technique, we establish some new oscillatory and asymptotic criteria. The established results on one hand extend some known results in the literature, on the other hand unify continuous and discrete analysis as two special cases of an arbitrary time scale. We also present some applications for the established results.
- Oscillation /
- asymptotic behavior /
- third order nonlinear delay dynamic equations /
- time scales
MSC: 34N05;26E70;34C10

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References

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