具有阻尼项的二阶非线性微分方程的区间振动准则

Interval Criteria for Oscillation of Second Order Nonlinear Differential Equations with Damping

中文关键词:  区间振动准则  二阶  非线性  阻尼  Riccati变换.

英文关键词:interval oscillation criteria  second order  nonlinear  damped  Riccati transformation.

中文摘要:

      本文研究一类具有阻尼项的二阶非线性微分方程, 利用平均函数和一个广义 Riccati 变换, 得到了该方程的新的区间振动准则, 这些准则不同于已知的依赖于整个区间 $[t_0,\infty )$ 的性质的结果, 而是仅依赖于区间 $[t_0,\infty )$ 的子区间列的性质. 所得结果推广和改进了Kong 的振动准则. 特别, 还给出了几个例子以说明本文所得结果的优越性.

英文摘要:

      In this paper, we investigate a class of second-order nonlinear differential equations with damping. By using averaging functions and a generalized Riccati transformation, new interval oscillation criteria for the differential equations are established, which are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of $[t_0,\infty )$, rather than on the whole half-line. Our results extend and improve some known results in the literature. In particular, several examples that dwell upon the sharp conditions of our results are also included.