Existence of solutions for a class of third-order two-point boundary value problems

doi:10.3785/j.issn.1008-9497.2024.03.003

Journal of Zhejiang University (Science Edition)

2024, Vol. 51

Issue (3): 273-276 DOI: 10.3785/j.issn.1008-9497.2024.03.003

Mathematics and Computer Science

Existence of solutions for a class of third-order two-point boundary value problems

Liyuan WANG(

),Ruyun MA(

)

School of Mathematics and Statistics，Xidian University，Xi'an 710126，Shaanxi Province，China

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Abstract

In this paper, we consider the boundary value problems of third-order nonlinear ordinary differential equation $u''' t = f (t, u (t), u' (t), u'' (t)), ?? a . e . ? 0 < t < 1, u 0 = u' 0 = u' 1 = 0,$ where $? f : [0 ， 1] × R 3 → R ?$ satisfies Carathéodory conditions. Under some suitable growth conditions on $f$ , we show that the above problem has at least one solution. The proof of the main results is based on Leray-Schauder fixed point theorem.

Key words： third-order ordinary differential equation boundary value problem Leray-Schauder fixed point theorem existence

Received: 06 March 2023 Published: 07 May 2024

CLC:

O 175.8

Corresponding Authors: Ruyun MA E-mail: wly13707667619@163.com;ryma@xidian.edu.cn

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Cite this article:

Liyuan WANG,Ruyun MA. Existence of solutions for a class of third-order two-point boundary value problems. Journal of Zhejiang University (Science Edition), 2024, 51(3): 273-276.

URL:

https://www.zjujournals.com/sci/EN/Y2024/V51/I3/273

一类三阶两点边值问题解的存在性

考察了三阶非线性常微分方程边值问题 $u''' t = f (t, u (t), u' (t), u'' (t)), ??? a . e . ? 0 < t < 1, u 0 = u' 0 = u' 1 = 0,$ 其中 $f : [0 ， 1] × R 3 → R ?$ 满足Carathéodory条件。在非线性项 $? f ?$ 满足适当增长性条件下，三阶非线性常微分方程边值问题至少存在1个解。基于Leray-Schauder不动点定理证明了主要结果。

关键词： 三阶常微分方程, 边值问题, Leray-Schauder不动点定理, 存在性


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