单边增长条件下2n阶常微分方程的奇周期解

Odd periodic solutions for 2n order ordinary differential equations under unilateral growth conditions

摘要:

本文讨论了一类2n阶微分方程周期解的存在性，其中 n 是正整数. 运用Leray-Schauder不动点定理与Fourier分析的方法，在允许非线性项f超线性增长的条件下，本文获得了该方程的奇周期解.

Abstract:

In this paper, we discuss the existence of odd periodic solutions for nonlinear 2nth-order differential equations. By applying the Leray-Schauder fixed point theorem and Fourier analysis method, the results of existence of odd peiodic solutions is obtained under the nonlinearity f satisfies unilateral growth condition.