一类中立型脉冲积分微分方程概周期解的存在性和唯一性  

On the Existence and Uniquess of Almost Periodic Solutions of a kind of Neutral and Impulsive Integro-differential Equations

作　　者：林远华[1] 俞元洪[2] 

机构地区：[1]河池学院数学与统计学院,广西宜州546300 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《数学的实践与认识》2014年第16期218-229,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361010);广西教育厅科研项目(201010LX463);河池学院统计学重点学科资助项目(院科研2013[2]号)

摘　　要：考虑具连续时滞和离散时滞的中立型脉冲积分微分方程去{d/dt[x(t)+q∑j=1ej(t)x(t-δj(t))]=A(t,x(t))x(t)+t∫-∞C(t,s)x(s)ds+p∑j=1gj(t,x(t=Ti(t)))+b(t),t≠tk,tk<tk+1,△x(t)=Bkx(t)+Ik(x(t))+γk,.t=tk,k∈Z.概周期解的存在性和唯一性问题.利用线性系统指数二分性理论和不动点定理,莸得了保证中立型系统概周期解存在性和唯一性的充分条件,推广了相关文献的主要结果.The existence and uniqueness of almost periodic solutions of neutral integrodifferential equations with both continuous and discrete delays and impulsive of the form {d/dx[x（t）＋q∑j=1ej（t）x（t-δj（t））]=A（t,x（t））x（t）＋t∫-∞C（t,s）x（s）ds＋p∑i=1gi（t,x（t-τi（t）））＋b（t）,t≠tk,tk〈tk＋1,△x（t）=Bkx（t）＋Ik（x（t））＋γk,t=tk,k∈Z are considered.By combining theory of exponential dichotomies of linear system and fixed point theorem, some sufficient conditions that guarantee the existence and uniqueness of almost periodic solutions of the system are obtained. The conclusions made in the relevant documents are extended.

关 键 词：时滞 概周期解 指数型二分性 不动点定理 

分 类 号：O175[理学—数学]