一类四阶常微分方程周期边值问题的可解性

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (2): 213-218.

一类四阶常微分方程周期边值问题的可解性

张丽娟, 李永祥

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2021-04-30 出版日期:2022-03-26 发布日期:2022-03-26
通讯作者: 李永祥 E-mail:liyx@nwnu.edu.cn

Solvability of Periodic Boundary Value Problems for a Class of Fourth-Order Ordinary Differential Equations

ZHANG Lijuan, LI Yongxiang

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2021-04-30 Online:2022-03-26 Published:2022-03-26

摘要/Abstract

摘要： 用Fourier分析法与Leray-Schauder不动点定理, 讨论四阶周期边值问题解的存在性与唯一性, 在非线性项f(x,u,v)满足适当的不等式条件下, 获得了该问题解的存在性与唯一性.

关键词: 四阶常微分方程, Fourier分析法, Leray-Schauder不动点定理

Abstract: By using Fourier analysis and Leray-Schauder fixed point theorem, we discuss the existence and uniqueness of solutions of the fourth-order periodic boundary value problem. The existence and uniqueness of the solution of the problem are obtained under the condition that the nonlinear term f(x,u,v) satisfies an appropriate inequality.

Key words: fourth-order ordinary differential equation, Fourier analysis, Leray-Schauder fixed point theorem

中图分类号:

O175.8

张丽娟, 李永祥. 一类四阶常微分方程周期边值问题的可解性[J]. 吉林大学学报(理学版), 2022, 60(2): 213-218.

ZHANG Lijuan, LI Yongxiang. Solvability of Periodic Boundary Value Problems for a Class of Fourth-Order Ordinary Differential Equations[J]. Journal of Jilin University Science Edition, 2022, 60(2): 213-218.

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[2]	李菊鹏, 李永祥. 一类n阶完全常微分方程边值问题解的存在性[J]. 吉林大学学报(理学版), 2019, 57(1): 9-14.