无穷区间上两类抽象无界函数族相对紧的判定及其应用  

THE DECISION THEOREMS OF RELATIVE COMPACTNESS FOR TWO CLASSES OF ABSTRACT FUNCTION GROUPS IN AN INFINITE INTERVAL AND ITS APPLICATIONS

作　　者：刘炳妹[1,2] 刘立山[1] 

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165 [2]中国矿业大学理学院,徐州221116

出　　处：《系统科学与数学》2010年第7期1008-1019,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助项目(10771117);曲阜师范大学博士科研启动经费资助项目(Bsqd2007040)

摘　　要：给出了无穷区间上抽象无界连续函数族和抽象无界可微函数族相对紧性判定的充要条件,并应用它获得了无穷区间上二阶微分方程两点边值问题无界解的存在性.In this paper,sufficient and necessary conditions are given for relative compactness of an abstract unbounded continuous function group and of an abstract differentiable function group.In terms of the results,the existence of unbounded solution for second-order boundary value problem in infinite interval are obtained.

关 键 词：相对紧 等度连续 无界解 

分 类 号：O174[理学—数学]