OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH A NONLINEAR NEUTRAL TERM ON TIME SCALES

Ying Sui; Zhenlai Han

doi:10.11948/2018.1811

2018 Volume 8 Issue 6

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2018 > 8(6): 1811-1820

Next Article Previous Article

Ying Sui, Zhenlai Han. OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH A NONLINEAR NEUTRAL TERM ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1811-1820. doi: 10.11948/2018.1811

Citation:

Ying Sui, Zhenlai Han. OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH A NONLINEAR NEUTRAL TERM ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2018, 8(6): 1811-1820. doi: 10.11948/2018.1811

OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH A NONLINEAR NEUTRAL TERM ON TIME SCALES

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Fund Project:

Abstract

Abstract

In this article, we consider the oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales. Some new sufficient conditions which insure that any solution of the equation oscillates are established by means of an inequality technique and Riccati transformation. This paper improves and generalizes some known results. Several illustrative examples are given throughout.
- Oscillation /
- neutral /
- time scales /
- dynamic equation
MSC: 34C10;34K40;26E70

FullText(HTML)

References

[1]	R. P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation of second order differential equations with a sublinear neutral term, Carpathian Journal of Mathematics, 2014, 30(1), 1-6. Google Scholar
[2]	M. Bohner, L. Erbe, A. Peterson, Oscillation for nonlinear second order dynamic equations on a time scale, Journal Mathematical Analysis Applications, 2005, 301, 491-507. Google Scholar
[3]	B. Baculiova, J. Dzrina, Oscillation theorems for second-order nonlinear neutral differential equations, Computers and Mathematics with Applications, 2011, 62(12),4472-4478. Google Scholar
[4]	M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser Boston, Boston, 2001. Google Scholar
[5]	S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math, 1990, 18, 18-56. Google Scholar
[6]	Z. L. Han, T. Li, S. Sun, Oscillation for second-order nonlinear delay dynamic equations on time scales, Advances in Difference Equations, 2009, 2009, 1-13. Google Scholar
[7]	B. G. Jia, L. Erbe, A. Peterson, An oscillation theorem for second order superlinear dynamic equations on time scales, Applied Mathematics and Computation, 2013, 219(20), 10333-10342. Google Scholar
[8]	B. G. Jia, L. Erbe, A. Peterson, Oscillation theorems for second order sublinear dynamic equations on time scales, Dynamics of Continuous, Discrete and Impulsive Systems Series A:Mathematical Analysis, 2012, 19(5), 615-626. Google Scholar
[9]	S. H. Saker, Oscillation of second-order nonlinear neutral delay dynamic equations on time scales, Journal of Computational and Applied Mathematics, 2006, 187(2), 123-141. Google Scholar