带有导数项的Neumann问题正解的存在性

Existence of positive solutions of a second-order Neumann problem with derivative term

本文研究了带有导数项的非线性Newmann问题{u"(t)+ku(t)=f(t,u(t),u'(t)),t∈(0,1),u'(0)=u'(1)=0正解的存在性,其中0<k≤π~2/4,f:[0,1]×R^+×R→R^+连续.当函数f(t,x,y)关于x和y满足一定的超线性增长条件及Nagumo条件时,本文得到了问题正解的存在性.主要结果的证明基于不动点指数理论.

Under the conditions that the nonlinear term f（t,x,y） is superlinear growth on x and y and satisfies Nagumo-type conditions, the existence of positive solutions of the following second-order New- mann problem with derivative terms u″（t）＋ku（t）=f（t,u（t）,u＇（t））,t∈（0,1）,u′（0）=u′（1）=0 is considered, where 0〈k≤π^2/4,f：[0,1]×R^＋×R→R^＋ is continuous. The proof is based on the fixed point index theory in cones