Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

作者：Zhang, Shao-Yan; Wang, Qi-Ru^*; Kong, Qingkai

来源：Applied Mathematics and Computation, 2016, 275: 324-334.

DOI：10.1016/j.amc.2015.11.084

• nth-order nonlinear dynamic equation
• Time scales
• Oscillation
• Asymptotics
• Generalized Riccati technique

This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form
(r(t)Phi(gamma)(chi(Delta n-1)(t)))(Delta) + Sigma(k)(i=0)q(i)(t)Phi alpha(i)(chi(delta(i)(t))) = 0
with n >= 2. By discussing the signs of nth-order derivatives of eventually positive solutions for i _ 1, ..., n - 1, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature.

• 出版日期2016-2-15
• 单位广东金融学院; 中山大学