一类延迟积分方程的伪概周期解的存在性  

Existence of pseudo almost periodic solutions for a delay integral equations

作　　者：陈丽岩[1] 姚慧丽[1] 

机构地区：[1]哈尔滨理工大学应用数学系,哈尔滨150080

出　　处：《哈尔滨商业大学学报（自然科学版）》2011年第5期747-750,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：黑龙江省自然科学基金项目(A9813)

摘　　要：利用伪概周期函数的定义及其相关性质和不动点定理,给出了一类延迟积分方程的伪概周期解的存在性定理,并证明了伪概周期解的概周期部分恰为其对应的概周期积分方程的概周期解.在一些文献对某些延迟积分方程的概周期解和渐近概周期解研究的基础上,探讨了其伪概周期解的存在条件,这样会使得到的结论应用的更加广泛.The main research contents of this paper was that almost periodic type functions were applied to this type of the delay integral equations,on the basis,existence of almost periodic type solutions for this type delay integral equations was discussed.By the definition of pseudo almost periodic functions and related properties as well as the theorem of fixed point,a theorem about the existence of pseudo almost periodic solutions for a type of delay integral equations was discussed.Consequently,it was proved that the almost periodic part of pseudo almost periodic solution is the almost periodic solution of corresponding almost periodic integral equation.On the basis of some literature for almost periodic solutions and asymptotically almost periodic solutions for some delay integral equations,existence conditions of pseudo almost periodic solutions were discussed.Thus,the conclusions which obtained were made to be used more widely.

关 键 词：伪概周期解 延迟积分方程 不动点 

分 类 号：O175[理学—数学]