2k阶非线性时滞微分方程的周期解

Periodic Solutions for(2k)th-Order Nonlinear Delay Differential Equations

应用Schauder不动点定理和傅氏分析技术,推广了二阶时滞微分方程周期解的结果,证明了2k阶非线性时滞微分方程在L2(0,2π)空间中2π周期解的存在性与惟一性.保证结果成立的条件是通常Lazer型非共振条件的自然推广.

Applying Schauder fixed-point theorem and Fourier＇ s method, we generalized the results on the existence and uniqueness of the periodic solutions for a class of second order delay differential equations, and gave the existence and uniqueness of 2π-periodic solutions for （2k）th-order nonlinear delay differential equations on space L^2 （0,2π）. The condition to ensure the theorems is a variety of usual Lazer type one.