## 留言板 引用本文: 雷策宇, 韩晓玲. 带变号格林函数的三阶三点边值问题的正解的存在性[J]. 华南师范大学学报（自然科学版）, 2021, 53(2): 104-109. LEI Ceyu, HAN Xiaoling. The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(2): 104-109. doi: 10.6054/j.jscnun.2021032
 Citation: LEI Ceyu, HAN Xiaoling. The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(2): 104-109. ## 带变号格林函数的三阶三点边值问题的正解的存在性

##### doi: 10.6054/j.jscnun.2021032

###### 通讯作者: 韩晓玲, Email: hanxiaoling9@163.com
• 中图分类号: O175.8

## The Existence of Positive Solutions to A Third-order Three-point Boundary Value Problem with Sign-changing Green's Function

• 摘要: 应用格林函数的性质和迭代法, 研究了一类具有变号格林函数的三阶三点边值问题 $\left\{ {\begin{array}{*{20}{c}} \begin{array}{l} u'''\left( t \right) = f\left( {t,u\left( t \right)} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( {t \in \left[ {0,1} \right]} \right),\\ u\left( 1 \right) = 0,u'\left( 0 \right) = u''\left( 0 \right),\alpha u''\left( \eta \right) + \beta u\left( 0 \right) = 0 \end{array} \end{array}} \right.$ 正解的存在性, 其中, fC([0, 1]×[0, ∞), [0, ∞)), α∈[0, 1], $\frac{2}{7}$α < β < $\frac{2}{3}$α, η∈[$\frac{2}{3}$, 1). 得到了该边值问题正解存在性的条件.
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##### 出版历程
• 收稿日期:  2020-08-02
• 网络出版日期:  2021-04-29
• 刊出日期:  2021-04-25

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