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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 32-37.doi: 10.6040/j.issn.1671-9352.0.2019.320

• • 上一篇    

带积分边界条件的四阶边值问题的单调正解

何燕琴,韩晓玲*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2019-12-11
  • 作者简介:何燕琴(1994— ), 女, 硕士研究生,研究方向为常微分方程边值问题. E-mail:1193360529@qq.com*通信作者简介:韩晓玲(1978— ),女,教授,博士生导师,研究方向为常微分方程边值问题. E-mail:hanxiaoling9@163.com
  • 基金资助:
    国家自然科学基金资助项目(11561063)

Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions

HE Yan-qin, HAN Xiao-ling*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-12-11

摘要: 运用单调迭代技巧研究了带积分边界条件的四阶边值问题{u(4)(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫10g(t)u″(t)dt单调正解的存在性,其中 f:[0,1]×[0,+∞)2→[0,+∞)连续, g:[0,1]→[0,+∞)连续,不仅获得了该问题正解的存在性,而且得出迭代列的初值是简单的零函数或一次函数。

关键词: 四阶边值问题, 积分边界条件, 单调正解, 存在性, 迭代技巧

Abstract: By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions{u(4)(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫10g(t)u″(t)dt,where f:[0,1]×[0,+∞)2→[0,+∞) is continuous, g:[0,1]→[0,+∞) is continuous, not only the existence of the positive solution of the problem is obtained, but also the initial value of the iterative sequence is a simple zero function or a primary function.

Key words: fourth-order boundary value problem, integral boundary condition, monotone positive solution, existence, iterative technique

中图分类号: 

  • O175.8
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