一阶多点边值问题多个解的存在性

doi:10.6040/j.issn.1671-9352.0.2015.434

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (6): 42-48.doi: 10.6040/j.issn.1671-9352.0.2015.434

一阶多点边值问题多个解的存在性

朱雯雯

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2015-09-14 出版日期:2016-06-20 发布日期:2016-06-15
作者简介:朱雯雯(1991— ), 女, 硕士研究生,研究方向为常微分方程边值问题.E-mail: zhuwenwen58@163.com
基金资助:
国家自然科学基金资助项目(11361054);甘肃省自然科学基金资助项目(1208RJZA258)

Existence of multiple of solutions of first order multi-point boundary value problem

ZHU Wen-wen

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

Received:2015-09-14 Online:2016-06-20 Published:2016-06-15

摘要/Abstract

摘要： 运用上下解方法和拓扑度理论研究了一阶常微分方程多点边值问题{u'(t)=f(t,u(t)), t∈［0,T］,u(0)+∑^m_k=1a_ku(t_k)=c多个解的存在性, 其中c∈R, t_k(k=1,2,3,…,m)满足 012<…mk<0 均为给定常数, 并且满足 1+∑^m_k=1a_k>0, f∈C(［0,T］×R,R)。实例说明了结果的正确性。

关键词: 多点边值问题, 上下解方法, 拓扑度理论

Abstract: We use the method of the upper and lower solutions and topological degree theory to study existence of multiple solutions of first order differential equations multi-point boundary value problem{u'(t)=f(t,u(t)), t∈［0,T］,u(0)+∑^m_k=1a_ku(t_k)=cwhere c∈R, t_k(k=1,2,3,…,m)satisfy 012<…mk<0 are constants, and 1+∑^m_k=1a_k>0, f∈C(［0,T］×R, R). Finally, an example is presented to illustrate the application of the obtained result.

Key words: topological degree theory, multi-point boundary value problem, upper and lower solutions

中图分类号:

O175.8

朱雯雯. 一阶多点边值问题多个解的存在性[J]. 山东大学学报（理学版）, 2016, 51(6): 42-48.

ZHU Wen-wen. Existence of multiple of solutions of first order multi-point boundary value problem[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 42-48.

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一阶多点边值问题多个解的存在性

Existence of multiple of solutions of first order multi-point boundary value problem

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