基于一类高阶微分方程的周期解的存在性研究

The existence of periodic solution based on high-order differential equation

一直以来,非线性微分方程的周期解的存在唯一性一直是研究的热点之一,在许多领域都有着十分广泛的应用。特别是一类高阶非线性微分方程,由于涉及领域广泛而倍受人们关注。该文讨论Schauder不动点方法,以及非线性泛函分析中的锥拉伸锥压缩方法,研究了微分方程的周期解的存在性问题。

For a long time,the existence of periodic solution of nonlinear differential equation is always one of the hot researches,have a very wide range of applications in many areas.Especially high-order nonlinear differential equation,attracts people's attention due to the extensive field.In this paper,we discuss the Schauder fixed point method,and the method of the compression and expansion of cone in nonlinear functional analysis,to discuss the existence of periodic solution of differential equations.