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

作者：文乾(西北师范大学数学与统计学院)；李永祥(西北师范大学数学与统计学院)

Author：WEN Qian(College of Mathematics and Statistics, Northwest Normal University)；LI Yong-Xiang(College of Mathematics and Statistics, Northwest Normal University)

收稿日期：2018-03-13 年卷（期）页码：2018,55(6):1167-1170

期刊名称：四川大学学报: 自然科学版

Journal Name：Journal of Sichuan University (Natural Science Edition)

关键字：单边增长；奇周期解；Leray-Schauder不动点定理；Fourier分析

Key words：Unilateral growth; Odd periodic solution; Leray-Schauder fixed point theorem; Fourier series expansion;

基金项目：国家自然科学基金(11661071)

中文摘要

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.

英文摘要

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.

【关闭】

论文摘要

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