迭代微分方程 x″(t)=f(x(x(t)))的初值问题

Initial Value Problem to the Differential iterative Equation x″(t)=f(x(x(t)))

利用 Schauder不动点定理 ,研究一类二阶自治迭代泛函微分方程 x″( t) =f( x( x( t) ) )强解的性态及满足初始条件 :x′( σ) =0 ,x( σ) =σ的 Cauchy问题饱和强解的存在性 .

By means of Schauder's fixed theorem, the paper deals with the behavior and existence of strong solutions to the second order functional iterative equation x″(t)=f(x(x(t))) and the existence of maximum strong solutions to the equation satisfying the initial conditions x(σ)=σ and \%x′(σ)=0 for any σ∈R .