一类三阶常微分方程无穷边值问题解的存在性

doi:10.13438/j.cnki.jdzk.2025.04.004

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (4): 19-27.DOI: 10.13438/j.cnki.jdzk.2025.04.004

一类三阶常微分方程无穷边值问题解的存在性

宋国鑫,苟海德,刘静芳

（1.兰州信息科技学院通识教育学院,甘肃兰州 730300；2.西北师范大学数学与统计学院,甘肃兰州 730070;3.兰州石化职业技术大学信息工程学院,甘肃兰州 730060）

出版日期:2025-07-25 发布日期:2025-08-05
作者简介:宋国鑫（1996—）,男,甘肃榆中人,兰州信息科技学院通识教育学院助教,硕士,主要从事常微分方程边值问题研究.
基金资助:
甘肃省自然科学基金资助项目（245RRA131）

Existence of Solutions for a Class of Third-Order Ordinary Differential Equations Boundary Value Problems on an Infinite Interval

SONG Guoxin,GOU Haide,LIU Jingfang

(1.College of General Education,Lanzhou University of Information Science and Technology,Lanzhou 730300,China；2.College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China;3.College of Information and Engineering,Lanzhou Petrochemical University of Vocational Technology,Lanzhou 730060,China)

Online:2025-07-25 Published:2025-08-05

摘要/Abstract

摘要：研究了一类无穷区间上的三阶常微分方程边值问题解的存在性.先选取适当的Banach空间,将边值问题等价转化为此空间中一类积分算子不动点的存在性问题,再利用推广的Arzelá-Ascoli定理证明了积分算子的全连续性,最后应用Leray-Schauder原理给出了边值问题解的存在性定理.

关键词： 三阶常微分方程, 无穷边值问题, Leray-Schauder原理, 存在性

Abstract: This paper investigates the existence of solutions for a class of third-order ordinary differential equation boundary value problems on an infinite interval.Firstly,the boundary value problems is equivalently transformed into the existence problems of fixed points for a class of integral operators in a suitable Banach space.Then,the complete continuity of the integral operators is proved by using the generalized Arzelá-Ascoli theorem.Finally,the Leray-Schauder principle are employed to establish an existence theorem of the solutions for this kind of boundary value problems.

Key words: third-order ordinary differential equations, boundary value problem on infinite intervals, Leray-Schauder principle, existence

宋国鑫, 苟海德, 刘静芳. 一类三阶常微分方程无穷边值问题解的存在性[J]. 吉首大学学报（自然科学版）, 2025, 46(4): 19-27.

SONG Guoxin, GOU Haide, LIU Jingfang. Existence of Solutions for a Class of Third-Order Ordinary Differential Equations Boundary Value Problems on an Infinite Interval[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(4): 19-27.

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一类三阶常微分方程无穷边值问题解的存在性

Existence of Solutions for a Class of Third-Order Ordinary Differential Equations Boundary Value Problems on an Infinite Interval

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