一类三阶非线性微分方程解的振动性  

Oscillation Criteria of Solution for a Class of Third Order Nonlinear Differential Equations

作　　者：赵玉萍[1] ZHAO Yuping(College of Mathematics and Statistics,Qinghai Nationalities University,810007,Xining,Qinghai,China)

机构地区：[1]青海民族大学数学与统计学院,青海西宁810007

出　　处：《淮北师范大学学报（自然科学版）》2024年第3期1-5,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金项目(12161071);青海省科技厅项目(2023-ZJ-949Q)。

摘　　要：为进一步发展和完善非线性微分方程解的振动理论,研究一类三阶非线性时滞微分方程解的振动性和渐近性。利用实分析、Riccati变换和不等式技巧获得该方程解振动或收敛于零的新的充分条件,估算该方程有正解时其值的大小,推广并改进相关文献中一些已知结果,并给出说明定理应用的例子。In order to develop and improve the theory about the oscillation criteria of solution of nonlinear differential equations,this paper is concerned with oscillation criteria of solution and asymptotic behavior of solutions for a class of third order nonlinear delay differential equations.By using real analysis,Riccati transformation and inequality techniques,some new sufficient conditions for all solutions to be oscillatory or asymptotically convergent to zero have been obtained,the size of the value when the equation has a positive solution is estimated.The result improves and extends some known results.An example is given to illustrate the result.

关 键 词：RICCATI变换 振动性 非线性 正解 时滞 

分 类 号：O175.7[理学—数学]