高维无穷时滞脉冲积分微分方程概周期解的存在唯一性

Existence and Uniqueness of Almost Periodic Solutions to the Higher Dimensional Integro-differential Equation with Impulses and Infinite Delay

研究一类高维无穷时滞的非线性脉冲积分微分方程x′(t)=A(t)x(t)+∫-t∞C(t,s)g(s,x(s))ds+f(t,x(t-τ))+b(t),t≠tkΔx(t)=Bkx(t)+Ik(x(t))+γk,t=tk,k∈Z概周期解的存在性、唯一性问题.利用不动点原理和线性系统的指数二分性理论,建立了保证其概周期解存在性、唯一性的充分条件,得到了一些新的结果.

A study is made on existence and uniqueness of almost periodic solutions to a class of nonlinear integro-differential equations with impulses and infinite delay of the following x′（t）=A（t）x（t）＋∫t-∞C（t,s）g（s,x（s））ds＋f（t,x（t-τ））＋b（t）,t≠tkΔx（t）=Bkx（t）＋Ik（x（t））＋γk,t=tk,k∈Z By using fixed point method and the theory of exponential dichotomy of linear system, some sufficient condition that guarantee the existence and uniqueness of almost periodic solution of the system are obtained, Some new results are obtained.