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

作　　者：黄秋语 孙莉 马婷婷 王广瓦 

机构地区：[1]江苏师范大学数学与统计学院,江苏 徐州

出　　处：《应用数学进展》2020年第3期293-300,共8页Advances in Applied Mathematics

基　　金：本文受国家自然科学基金项目(NSFC11501260),江苏高校优势学科建设工程项目(PAPD),江苏高校品牌专业建设工程资助项目(PPZY2015A013)和江苏省大学生创新创业训练计划项目(201810320015Z)资助。

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。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.

关 键 词：区间振动 参数方程 RICCATI变换 多时滞 微分方程 

分 类 号：O17[理学—数学]