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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (9): 69-75.doi: 10.6040/j.issn.1671-9352.0.2016.506

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带有导数项的二阶周期问题正解

闫东亮   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2016-11-03 出版日期:2017-09-20 发布日期:2017-09-15
  • 作者简介:闫东亮(1990— ), 女, 硕士研究生,研究方向为常微分方程边值问题.E-mail: yhululu@163. com
  • 基金资助:
    国家自然科学基金资助项目(11671322);数学天元基金资助项目(11626061)

Positive solutions of a second order periodic problems with derivative terms

YAN Dong-liang   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2016-11-03 Online:2017-09-20 Published:2017-09-15

摘要: 获得了非线性函数带有导数项的二阶周期边值问题{u″(t)+au(t)=f(t,u(t),u'(t)),〓t∈[0,1],u(0)=u(1), u'(0)=u'(1)正解的存在性, 其中(π2)/4π2, f:[0,1]×R+×R→R+连续。 f(t,x,y)满足Nagumo条件, 且关于 x 和 y 满足一定的超线性增长条件。针对超线性情形, Nagumo条件关于y严格控制了f的增长。主要结果的证明基于不动点指数理论。

关键词: 正解, 不动点指数理论, 二阶周期边值问题

Abstract: This paper shows the existence of positive solutions of the fully second-order periodic boundary value problem {u″(t)+au(t)=f(t,u(t),u'(t)), t∈[0,1],u(0)=u(1), u'(0)=u'(1),where(π2)/42, f:[0,1]×R+×R→R+ is continuous. f(t,x,y) is superlinear growth on x and y and a Nagumo-type condition is presented. Under the conditions that the superlinear case, the Nagumo-type condition is restrict the growth of f on y. Our discussion is based on the fixed point index theory in cones.

Key words: positive solution, fixed point index theory, second-order boundary value problem

中图分类号: 

  • O175.8
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