摘要
考察了一类奇异二阶周期边值问题,其中非线性项f(t,u)是局部Caratheódory函数.主要工具是高度函数,它描述了非线性项f(t,u)在有界集合上的增长特性.通过考察高度函数的积分获得了单个或多重正解存在的几个充分条件.我们的工作表明这种存在性与非线性项f(t,u)在u=0附近的性质无关.
A class of singular second-order periodic boundary value problems is considered where the nonlinear term f（t, u） is a local Caratheódory function. Main tools are the height functions that describe the growth feature of nonlinear term f（t, u） on bounded set. Several sufficient conditions to guarantee the existence of single or multiple positive solutions are obtained by considering the integrations of height functions. Our work shows that the existence is independent of the properties of nonlinear term f（t, u） near u = 0.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第6期1357-1364,共8页
Acta Mathematica Sinica：Chinese Series
关键词
奇异常微分方程
周期边值问题
正解
singular ordinary differential equation
periodic boundary value problem
positive solution
