具有非线性导数项的二阶常微分方程的正周期解  

Positive Periodic Solutions of Second-Order Ordinary Differential Equations with Nonlinear Derivative Terms

作　　者：刘晓明 李永祥 LIU Xiaoming;LI Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2023年第6期1243-1250,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061062,11661071)。

摘　　要：用正算子扰动方法和锥上的不动点指数理论讨论具有非线性导数项的二阶常微分方程-u″(t)+a(t)u(t)=f(t,u(t),u′(t)),t∈ℝ正2π-周期解的存在性,其中:a:ℝ→(0,+∞)连续,以2π为周期;f:ℝ×[0,+∞)×ℝ→[0,+∞)连续,f(t,x,y)关于t以2π为周期.在非线性项f(t,x,y)满足适当的不等式条件下,得到了该方程正2π-周期解的存在性.We discuss the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term-u″(t)+a(t)u(t)=f(t,u(t),u′(t)),t∈ℝby using positive operator perturbation method and fixed point index theory in cones,where a:ℝ→(0,+∞)is a continuous 2π-periodic function,f:ℝ×[0,+∞)×ℝ→[0,+∞)is continuous,and f(t,x,y)is 2π-periodic with respect to t.Under certain inequality conditions of the nonlinear term f(t,x,y),we obtain the existence of positive 2π-periodic solutions of the equation.

关 键 词：二阶常微分方程 非线性导数项 正2π-周期解 闭凸锥 不动点指数 

分 类 号：O175.14[理学—数学]