带有导数项的二阶周期问题正解

Positive solutions of a second order periodic problems with derivative terms

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π~2/4<a≤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。

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） , whereπ^2/4〈a≤π^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 off on y. Our discussion is based on the fixed point index theory in cones.