一类具有两个偏差变元的高阶微分方程反周期解的存在唯一性

摘要

Some sufficient conditions of the existence and uniqueness of anti-periodic solutions for a class of high-order differential equation with two deviating arguments as follows x（n） (t) + f(t,x1 (t) ,x″(t) , … ,x(n-1) (t) ) + g1 (t,x(t - τ1 (t) ) ) + g2 (t ,x(t - τ2 (t) ) ) = e(t) is obtained by employing Leray-Schauder degree theorem.%利用Leray-Schauder度理论,获得一类具有两个偏差变元的高阶微分方程x(n)(t)+f(t,x'(t),x''(t),…,x(n-1)(t))+g1(t,x(t-r1(t)))+g2(t,x(t-r2(t)))=e(t)反周期解存在唯一性的充分条件.