迭代微分方程x(t)=sum(ai(t)fi(x()(t))) from i=1 to n解的存在性

The existence of solutions to differential-iterative equations x(t)=sum(ai(t)fi(x()(t))) from i=1

摘要: 首先通过构造一个连续函数集合上的连续自映射的方法 ,利用 Schauder不动点定理 ,证明了一类二阶自迭代泛函微分方程 x" ( t) = ni=1 ai( t) fi( x( t) )满足初始条件 x(ξ) =η,x′(ξ) =0 ,ξ,η∈ R的周期解的存在性 .其次将该解 x( t)延拓至 ( -∞ ,∞ ) ,从而证明了所给方程在所给条件下具有满足初始条件 x( ξ) =η,x′(ξ) =0 ,ξ,η∈ R的周期解 x( t) ,t∈ ( -∞ ,∞ )

Abstract: First,by means of building a continuous map into itself to the set of continuous functions and Schauder's fixed theorem,this paper proves the existence of periodic solutions to a type of second order nonautonomous differential iterative equations x"(t)=ni=1a i(t)f i(x (t)) satisfying the initial condition x(ξ)=η and x′(ξ)=0 for any ξ and η∈R,second,the solution x(t) is continued to(-∞,+∞).The paper also proves that the given equation has periodic solutions x(t)satisfying the initial condit...