Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 234, pp. 1-17.

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

Authors:  Xun-Huan Deng (Sun Yat-Sen Univ., Guangzhou, China)
          Qi-Ru Wang    (Sun Yat-Sen Univ., Guangzhou, China)

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.