一类脉冲微分方程正周期解存在的充要条件

A Sufficient and Necessary Condition for the Existence of the Positive Periodic Solutions of a Class of Impulsive Differential Equations

考虑非线性脉冲微分方程x′(t)=x(t)[a(t)-b(t)x^p(t)],t≠t_k,△x|t=t_k=C_kx(t_k),k∈N.得到了该方程存在正周期解的充要条件为Π_(k=1)~m(1+c_k)~p exp(p∫_0^(?) a(σ)dσ)>1.

Consider the nonlinear impulsive differntial equation{x＇（t）=x（t）[a（t）-b（t）x^p（t）],t≠tk, △x｜t=tk=ckx（tk）,k∈N.A stdiicient and necessary condition obtained for the existence of the positive periodic solution is m∏k=1（1＋ck）^pexp（p∫^w 0）a（σ）dσ）〉1.