一类3阶非线性时滞微分方程振动解的存在性  

Existence of Oscillation Solution for a Family of Third Order Delay Nonlinear Differential Equations

作　　者：赵玉萍[1] 傅华 ZHAO Yuping;FU Hua(College of Mathematics and Statistics,Qinghai Nationalities University,Xining 810007,China;FuJian Police College,Fuzhou 350007,China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007 [2]福建警察学院,福州350007

出　　处：《重庆理工大学学报（自然科学）》2021年第1期236-240,共5页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11761056);青海民族大学校级项目(2021XJGH09)。

摘　　要：为了进一步发展和完善微分方程的振动理论,研究了一类3阶非线性时滞微分方程振动解的存在性。利用Schauder-Tychonoff不动点定理及一些分析技巧,获得了该类方程振动解存在的充分条件,并研究了这类方程的特殊形式非振动解存在的充分条件,丰富了微分方程的振动理论,给出了应用举例。In order to develop and improve the theory about oscillation of differential equations,the existence of oscillation solution for a family of third order delay nonlinear differential equations is studied.A sufficient condition for the existence of oscillation solution of the equations is obtained by Schauder-Tychonoff fixed point theorem and some necessary analytic techniques.A sufficient condition for existence of oscillation solution of special case of the equation is also studied.The oscillation theory of differential equation is enriched,and an application example is given.

关 键 词：微分方程 非线性 振动解 Schauder-Tychonoff定理 

分 类 号：O175.7[理学—基础数学]