Asymptotic properties of solutions of certain third-order dynamic equations

作者：Wang, Yuanfeng; Xu, Zhiting^*

来源：Journal of Computational and Applied Mathematics, 2012, 236(9): 2354-2366.

DOI：10.1016/j.cam.2011.11.021

• Oscillation
• Nonlinear dynamic equations
• Third order
• Time scale

In this paper, the well known oscillation criteria due to Hille and Nehari for second-order linear differential equations will he generalized and extended to the third-order nonlinear dynamic equation
(r(2)(t)((r(1)(t)x(Delta)(t))(Delta))(gamma))(Delta) q(t)f(x(t)) = 0
on time scale T, where gamma >= 1 is a ratio of odd positive integers. Our results are essentially new even for third-order differential and difference equations, i.e., when T = R and T = N. Two examples of dynamic equations on different time scales are given to show the applications of our main results.

• 出版日期2012-3
• 单位华南师范大学