一类差分方程的C^m解的存在性和惟一性(英文)

Existence and uniqueness of C^m solutions of a kind of difference equations

讨论了一类较广泛的差分方程G(x,f(x),f(x+1),…,f(x+n))=0,x∈R,其中G∈Cm(Rn+2,R),n≥2.通过采用小挪动映射逼近不动点的方法,对任一整数m≥0,在较弱的条件下证明了该方程的Cm解的存在性和惟一性.

This paper discusses a relatively general class of difference equationsG(x,f(x),f(x+1),...,f(x+n))=0,for all x∈R, where G∈Cm(Rn+2,R),and n≥2.Using the method of approximating fixed points by small shift of maps,the existence and uniqueness of Cm solutions of the above equation for any integer m≥0 under relatively weak conditions are proved.