带有导数项的二阶周期问题正解

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。

Positive solutions of a second order periodic problems with derivative terms

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.