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### 带有导数项的二阶周期问题正解

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

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.

• O175.8
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