Electron. J. Diff. Equ., Vol. 2013 (2013), No. 234, pp. 1-17.

Oscillation and nonoscillation for second-order nonlinear neutral functional dynamic equations on time scales

Xun-Huan Deng, Qi-Ru Wang

Abstract:
In this article, we investigate the oscillation and nonoscillation of second order nonlinear neutral dynamic equations with retarded and advanced arguments by means of the theory of upper and lower solutions for related dynamic equations along with some additional estimates on positive solutions. We also apply the Kranoselskii's fixed point theorem to obtain nonoscillation results. Some interesting examples are given to illustrate the versatility of our results.

Submitted April 9, 2013. Published October 22, 2013.
Math Subject Classifications: 34N05, 34K40, 34K11.
Key Words: Nonlinear neutral dynamic equations; oscillation; nonoscillation; upper and lower solutions; Kranoselskii's fixed point theorem.

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Xun-Huan Deng
School of Mathematics and Computational Science
Sun Yat-Sen University
Guangzhou 510275, China
email: deng_xunhuan@163.com
Qi-Ru Wang
School of Mathematics and Computational Science
Sun Yat-Sen University
Guangzhou 510275, China
email: mcswqr@mail.sysu.edu.cn

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