一类非线性泛函微分方程解的有界性

本文讨论连续函数空间 C 上的非线性泛函微分方程{d/(dt) X(t)=F(X_t)t≥0 X_0=φ∈C}的解的有界性。证明了当 F(φ)=-φ(0)G(φ),这里 G(φ)≠0对φ≠0,φ∈C 时,解 x(t,φ)具有性质:X(t,φ)≤φ(O)。

The Boundedness of Solutions for a Class of Nonlinear Functional Differential Equations

By using Lyapunov method of nonliear semigroups,We give out a resulte of boundedness for the solutions of equation {d/dt X(t)=F(X_t) t≥0 x_0=φ∈C(-r,0;R)} (*) that,if F has form F(φ)=-φ(O)G(φ)where φ∈C,G(φ)is nonnegative functional with property G(φ)≠0 for φ≠0,then the solution of(*),x(t, φ)satisfies |x(t,φ)≤|φ(0)|, t≥0