四阶微分方程奇异边值问题解的唯一性

doi:10.6040/j.issn.1671-9352.0.2016.027

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (2): 73-76.doi: 10.6040/j.issn.1671-9352.0.2016.027

四阶微分方程奇异边值问题解的唯一性

崔玉军,赵聪

山东科技大学数学与系统科学学院, 山东青岛 266590

收稿日期:2016-01-19 出版日期:2017-02-20 发布日期:2017-01-18
作者简介:崔玉军(1972— ), 男, 博士, 教授, 研究方向为非线性泛函分析. E-mail:sdustcyj@163.com
基金资助:
国家自然科学基金资助项目(11371221,11571207);高等学校博士学科点专硕科研基金(20123705110001);泰山学者优势特色学科人才团队支持计划资助项目;山东省高校科研创新团队资助

Uniqueness of solution for singular boundary value problems of fourth-order differential equations

College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

Received:2016-01-19 Online:2017-02-20 Published:2017-01-18

摘要/Abstract

摘要： 讨论了奇异边值问题{x⁽⁴⁾(t)-h(t)f(x(t))=0, 00-范数以及压缩映射原理来给出上述边值问题的唯一解。

关键词: 唯一解, 压缩映射原理, u₀-范数, 奇异边值问题

Abstract: We investigate the uniqueness of solution for{x⁽⁴⁾(t)-h(t)f(x(t))=0, 0h(t) is allowed to be singular at both t=0 and t=1. The main novelty of this paper is that the Lipschitz constant is related to the first eigenvalues corresponding to the relevant operators. We show the uniqueness of solution by applying the u₀-norm and contraction mapping principle.

Key words: uniqueness of solution, u0-norm, contraction mapping principle, singular boundary value problem

中图分类号:

O175.8

崔玉军,赵聪. 四阶微分方程奇异边值问题解的唯一性[J]. 山东大学学报（理学版）, 2017, 52(2): 73-76.

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四阶微分方程奇异边值问题解的唯一性

Uniqueness of solution for singular boundary value problems of fourth-order differential equations

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