一类奇异二阶边值问题的正周期解  

Positive Periodic Solutions of a Class of Singular Second-Order Boundary Value Problems

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《数学学报（中文版）》2007年第6期1357-1364,共8页Acta Mathematica Sinica：Chinese Series

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.

关 键 词：奇异常微分方程 周期边值问题 正解 

分 类 号：O175.8[理学—数学]