一类二阶非线性多时滞微分方程的区间振动准则
Interval Oscillation Criteria for a Class of Second-Order Nonlinear Differential Equations with Multiple Time-Varying Delays
DOI: 10.12677/AAM.2020.93035, PDF,    国家自然科学基金支持
作者: 黄秋语, 孙 莉, 马婷婷, 王广瓦：江苏师范大学数学与统计学院，江苏 徐州
关键词: 区间振动；参数方程；Riccati变换；多时滞；微分方程；Interval Oscillation； Parameter Function； Riccati Transform； Multiple Time-Varying Delays； Differential Equations
摘要: 引入参数函数，结合数学分析中的积分方法和完全平方法以及Riccati变换，得到一类二阶非线性多时滞微分方程的新的区间振动准则。该振动准则更具有一般性。区别于已知依赖于整个大区间的性质结果，这里得出的振动准则是仅仅依赖于该区间上的子区间列的性质。我们还给出了一个例子说明主要结果的有效性。
Abstract: By introducing parameter function, combined with the integral method in mathematical analysis and complete square method and Riccati transform, some new interval oscillation criteria for a class of second-order nonlinear differential equations with multiple time-varying delays are obtained. The oscillation criteria are more general. These results are different from most known ones in the sense that they are based on the information only on a sequence of sub-intervals of Ι=[t0,∞], rather than on the whole half-line. An example is given to illustrate the feasibility of the main results.
文章引用：黄秋语, 孙莉, 马婷婷, 王广瓦. 一类二阶非线性多时滞微分方程的区间振动准则[J]. 应用数学进展, 2020, 9(3): 293-300. https://doi.org/10.12677/AAM.2020.93035

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