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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (2): 155-158    DOI: 10.3785/j.issn.1008-9497.2020.02.004
数学与计算机科学     
一类完全四阶边值问题解的存在性
陈雪春, 李永祥
西北师范大学 数学与统计学院，甘肃 兰州 730070
Existence of solutions for a class of fully fourth-order boundary value problems
CHEN Xuechun, LI Yongxiang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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摘要： 讨论完全四阶两点边值问题$ \begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),t∈[0,1], \\ u(0)=u(1)=u''(0)=u''(1)=0 \end{cases}$解的存在性，其中 $f:[0,1]×R^{4}→R$为连续函数。在不限制非线性项的增长条件，也不假定非负的一般情形下，$f(t,x_{0},x_{1},x{2},x_{3})$关于$x_{3}$满足Nagumo 型条件时，运用截断函数技巧和上下解方法讨论了该问题解的存在性。
关键词： 完全四阶边值问题;  下解;  上解;  Nagumo型条件    
Abstract: In this paper, the existence of solutions for a class of fully fourth-order boundary value problem $\begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),t∈[0,1], \\ u(0)=u(1)=u''(0)=u''(1)=0 \end{cases}$ is discussed,where $f:[0,1]×R^{4}→R$ is a continuous function. Without restricting the growth condition of nonlinear terms and without assuming that they are non-negative in the general case, when $f(t,x_{0},x_{1},x{2},x_{3})$ satisfies the proper Nagumo-type condition on $x_{3}$, we obtain the existence of solutions for this equation via a truncating function and the lower and upper solution method.
Key words: fully fourth-order boundary value problem    lower solutions    upper solutions    Nagumo-type condition
收稿日期: 2018-12-23 出版日期: 2020-03-25
CLC:  O175.15  
基金资助: 国家自然科学基金资助项目(11261053,11661071).
通讯作者: ORCID:http:// orcid.org/0000-0002-5193-030X，E-mail:liyx@nwnu.edu.cn.     E-mail: liyx@nwnu.edu.cn
作者简介: 陈雪春(1994―)，ORCID:http:// orcid.org/0000-0002-0841-2566，女，硕士研究生，主要从事非线性泛函反分析研究，E-mail:18294473834@163.com.
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引用本文:

陈雪春, 李永祥. 一类完全四阶边值问题解的存在性[J]. 浙江大学学报（理学版）, 2020, 47(2): 155-158.

CHEN Xuechun, LI Yongxiang. Existence of solutions for a class of fully fourth-order boundary value problems. Journal of Zhejiang University (Science Edition), 2020, 47(2): 155-158.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.02.004    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I2/155

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