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.
出处
《数学的实践与认识》
CSCD
北大核心
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)
关键词
时滞
概周期解
指数型二分性
不动点定理
delay
almost periodic solution
exponential dichotomies
the fixed point theorem
