Oscillation of second-order quasi-linear neutral functional dynamic equations with distributed deviating arguments

Volume 4, Issue 3, pp 180--192 http://dx.doi.org/10.22436/jnsa.004.03.01

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Authors

Tongxing Li - School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China. - School of mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China. Ethiraju Thandapani - Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, India.

Abstract

In this paper, some sufficient conditions for the oscillation of second-order nonlinear neutral functional dynamic equation \[( r(t) ( [x(t) + p(t)x[\tau (t)]]^\Delta)^\gamma )^\Delta +\int^b_a q(t; \xi)x^\gamma [g(t; \xi)]\Delta\xi= 0; t \in \mathbb{T}\] are established. An example is given to illustrate an application of our results.

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Keywords

• Oscillation
• Second-order nonlinear equation
• Neutral dynamic equation
• Distributed deviating arguments
• Time scale.

MSC

•  34C10
•  34K11

References

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