一类泛函方程的连续解

On the Continuous Solutions for a Class of Functional Equations

本文考虑泛函方程x（x（t））＋f（x（t）-t）=0，在f满足一定单调性的条件下讨论了此方程连续解的性质、解的存在性和延拓性．其结果对于求解相应的泛函微分方程具有直接的应用．

Consider functional equation x(x(t) ) + f(x(t) -t) = 0 where f is continuous and mono-tone, and tim f(x) = 0, tim f(x) = + ∞. We discuss the behavior of continuous solutions of the equation, the existence and continuation of the solutions are also studied. These results can directly apply to functional differential equations for seeking solutions.