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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (8): 102-110.doi: 10.6040/j.issn.1671-9352.0.2019.725

• • 上一篇    

一类含一阶导数的四阶边值问题正解的全局结构

张亚莉   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2020-07-14
  • 作者简介:张亚莉(1995— ), 女, 硕士研究生, 研究方向为常微分方程边值问题. E-mail:zhangyali359@163.com
  • 基金资助:
    国家自然科学基金资助项目(11671322)

Global structure of the positive solution for a class of fourth-order boundary value problems with first derivative

ZHANG Ya-li   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-07-14

摘要: 考察了一类含一阶导数的四阶边值问题{u(4)(t)=rf(t,u(t),u'(t)), t∈(0,1),u(0)=u'(0)=u″(1)=u(1)=0正解的全局结构,其中r是正参数, f:[0,1]×[0,∞)×[0,∞)→[0,∞)连续,且f(t,0,0)=0。当参数r在一定范围内变化时,运用Rabinowitz全局分歧定理获得了该问题正解的全局结构,所得结果推广并改进了已有的相关结果。

关键词: 四阶, 正解, 主特征值, 分歧定理

Abstract: This paper considers the global structure of positive solutions for a fourth-order boundary value problem with first derivative{u(4)(t)=rf(t,u(t),u'(t)), t∈(0,1),u(0)=u'(0)=u″(1)=u(1)=0,where r is a positive parameter, f:[0,1]×[0,∞)×[0,∞)→[0,∞)is continuous, and f(t,0,0)=0. When the parameter r changes in a certain range, the global structure of positive solutions of the problem are obtained by using the Rabinowitz global bifurcation theorems. The conclusions in this paper generalize and improve the related results.

Key words: fourth-order, positive solution, principal eigenvalue, bifurcation theorem

中图分类号: 

  • O175.8
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