一类中立型积分微分方程概周期解的存在性和唯一性  

ON the Existence and Uniqueness of Almost Periodic Solutions of a Kind of Neutral Integro-differential Equtions

作　　者：林远华[1,2] 冯春华[2] 

机构地区：[1]河池学院数学系,广西宜州546300 [2]广西师范大学数学科学学院,广西桂林541004

出　　处：《河池学院学报》2008年第5期21-25,共5页Journal of Hechi University

基　　金：广西教育厅科研基金资助项目(编号:200708LX163);河池学院应用数学重点学科资助项目(院科研〔2007〕2号)

摘　　要：考虑具连续时滞和离散时滞的中立型积分微分方程d/dtx(t)+sum from j=1 to q ej(t)x(t-δj(t))=A(t)x(t)+∫from -∞ to t C(t,s)x(s)ds+sum from j=1 to q gi(t,x(t-τi(t)))+b(t)概周期解的存在性和唯一性问题.利用线性系统指数型二分性理论和压缩映射原理,获得了保证中立型系统概周期解存在性和唯一性的一组充分条件,推广了相关文献的主要结果.The existence and uniqueness of almost periodic solutions of neutral integro - differential equations with both continuous and discrete delays of the formd/dt[x（t）＋^q∑j=1 ej（t）x（t-δj（t））]=A（t）x（t）＋^t∫-∞C（t,s）x（s）ds＋^p∑i=1gi（t,x（t-τi（t）））＋b（t）are dealt with by combining the theory of exponential dichotomies of linear system and fixed point theorem, a set of sufficient conditions that guarantee the existence and uniqueness of almost periodic solutions of the system are ob- tained. Thus the conclusions made in the relevant documents are extended.

关 键 词：时滞 概周期解 指数型二分性 

分 类 号：O175.1[理学—数学]