一类三阶非线性微分方程周期边值问题解的存在性

Existence of solutions for a class of third-order nonlinear ordinary differential equations with periodic boundary value

作者：邓正平(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：DENG Zheng-Ping(College of Mathematics and Statistics, Northwest Normal University)；LI Yong-Xiang(College of Mathematics and Statistics, Northwest Normal University)

收稿日期：2018-10-22 年卷（期）页码：2019,56(5):792-796

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：三阶周期边值问题; Fourier级数; Leray-Schauder~不动点定理

Key words：Third-order periodic boundary value problem; Fourier series; Leray-Schauder fixed point theorem

基金项目：国家自然科学基金(11261053, 11661071)

中文摘要

本文讨论了一类三阶常微分方程周期边值问题解的存在性. 在非线性项满足适当的增长条件下,本文应用Fourier分析法与Leray-Schauder不动点定理获得了该问题解的存在唯一性结果.

英文摘要

In this paper, the existence of solutions for a class of third-order ordinary differential equation with periodic boundary value is considered. By applying the Fourier~analysis method and Leray-Schauder fixed point theorem, the existence and uniqueness of the solutions of the equation are obtained under the nonlinear term satisfies the proper growth conditions.

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论文摘要

一类三阶非线性微分方程周期边值问题解的存在性

Existence of solutions for a class of third-order nonlinear ordinary differential equations with periodic boundary value