%0 Journal Article
%T 带有导数项的二阶周期问题正解<br>Positive solutions of a second order periodic problems with derivative terms
%A 闫东亮
%J 山东大学学报（理学版）
%D 2017
%R 10.6040/j.issn.1671-9352.0.2016.506
%X 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)/4 π 2, 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。<br>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)/4 2, 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
%K 正解
%K 不动点指数理论
%K 二阶周期边值问题
%K &lt
%K br&gt
%K positive solution
%K fixed point index theory
%K second-order boundary value problem
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2016.506