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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (7): 16-21.doi: 10.6040/j.issn.1671-9352.0.2019.788

• • 上一篇    

一类四阶周期边值问题解的存在性与唯一性

王天祥,李永祥*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2020-07-08
  • 作者简介:王天祥(1992— ),男,硕士研究生,研究方向为非线性泛函分析. E-mail:wangtx1453071783@163.com*通信作者简介:李永祥(1963— ),男,博士,教授,博士生导师,研究方向为非线性泛函分析. E-mail:liyx@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11661071)

Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems

WANG Tian-xiang, LI Yong-xiang*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-07-08

摘要: 运用Leray-Schauder 不动点定理,讨论四阶周期边值问题{u(4)(t)=f(t,u(t), u'(t)), t∈[0,1],u(i)(0)=u(i)(1), i=0,1,2,3解的存在性与唯一性,其中f:[0,1]×R2→R连续。在允许非线性项f(t,x,y)关于x、y超线性增长的不等式条件下,获得了该问题解的存在性与唯一性。

关键词: 四阶周期边值问题, 存在性与唯一性, 超线性增长, Leray-Schauder不动点定理

Abstract: By using Leray-Schauder fixed point theorem, this paper discusses the existence and uniqueness of solutions for the fourth-order periodic boundary value problem{u(4)(t)=f(t,u(t),u'(t)), t∈[0,1],u(i)(0)=u(i)(1), i=0,1,2,3,where f:[0,1]×R2→R continuous. existence and uniqueness of solutions is obtained under the inequality conditions that allow the nonlinear term f(t,x,y) to grow superlinearly on x and y.

Key words: fourth-order periodic boundary value problem, existence and uniqueness, superlinear growth, Leray-Schauder fixed point theorem

中图分类号: 

  • O175.8
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