一类迭代差分方程连续解的全局存在性

Global Existence of Continuous Solutions to a Class of Iterative-difference Equations

针对N.Brillouёt-Belluot的公开问题所涉及的迭代差分方程,在局部有界连续解工作的基础上,研究一类形式更一般的迭代差分方程φ2(x)=λφ(kx+a)+f(x),其中φ为未知函数.利用不动点方法给出了该方程在R上存在无界连续解的条件.

To the iterative-differenee equation which relates to N. Brillouet-Belluot＇ s open problem, the local bounded continuous solutions of it had been discussed before. On the basis of this, in this paper we discuss a more general class of iterative-difference equations： φ^2 （x） = λφ（kx ＋ a） ＋f（x）, where φ is the unknown function. By applying a Faxed point theorem, the existence of their unbounded continuous solutions on R is proved.