一类单参数二阶周期边值问题正解的存在性

Existence of positive solutions for a class of second order periodic boundary value problems with one parameter

本文研究了非线性二阶常微分方程周期边值问题{u″+a(t,u)u=λg(t)f(u),t∈[0,T],u(0)=u(T),u′(0)=u′(T)正解的存在性,其中λ是一个正参数,a:[0,T]×[0,∞)→R+为L^p-Carathéodory函数,g:[0,T]→[0,∞),f:[0,∞)→[0,∞)为连续函数.主要结果的证明基于锥上的不动点指数理论.

In this paper,we consider the existence of positive solutions for the following nonlinear second-order ordinary differential equation with periodic boundary values:{u″+a(t,u)u=λg(t)f(u),t∈[0,T],u(0)=u(T),u′(0)=u′(T),whereλis an positive parameter,a:[0,T]×[0,∞)→R+is a L^p-Carathéodory function,g:[0,T]→[0,∞),f:[0,∞)→[0,∞)are continuous functions.The proof of the main results is based on the fixed point index theory on cones.