考虑具连续时滞和离散时滞的中立型积分微分方程d/(dt)[x(t)+sum from j=1 to q e_j(t)x(t-δ_j(t))]=A(t,x(t))x(t)+integral from -∞to t C(t,s)x(s)ds+sum from i=1 to l gi(t,x(t-τ_i(t)))+b(t)和d/(dt)[x(t)+sum from j=1 to q e_j(t)x(t-δ_j(t))]=A(t)x(t)+integral from -∞to t C(t,s)x(s)ds+sum from i=1 to l gi(t,x(t-τ_i(t)))+b(t)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泛函分析方法,并通过技巧性代换获得了保证中立型系统周期解存在性和唯一性的充分性条件,从而避开了在研究中立型系统时x(t-δ)时滞项的导数x′(t-δ)的出现,推广了相关文献的主要结果.
In this paper, by fixed point theorem of Krasnoselskii, we study the positive pe- riodic solution to a class of nonautonomous differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results on the existence of positive periodic solution to the equation are obtained.
Zhang Suping (Dept. of Math. and Physics, Anhui Institute of Architecture and Industry, Hefei 230022) Jiang Wei (School of Mathematical Science, Anhui University, Hefei 230039)
