一阶半线性中立型发展方程的适度解

Mild Solution of First Order Semilinear Neutral Evolution Equation

为了讨论Banach空间中带局部初始条件u(0)=h(u)+u_(0)的一种半线性中立型微分方程d/du[u(t)+g(t,u(t))]=Au(t)+f(t,u(t))的适度解问题,文章利用不动点原理证明了在h弱于紧性的条件下该方程适度解的存在性,并给出了h的几种弱于紧性的条件.

Based on the local initial conditions u(0)=h(u)+u_(0)in Banach Spaces,mild solution for a semilinear neutral form of differential equation d/du[u(t)+g(t,u(t))]=Au(t)+f(t,u(t))is discussed in this paper.The fixed point theorem is used to solve the mild solution when h is weaker than compactness.This paper also gives some conditions which are weaker than compactness.