Banach空间算子方程mild解

The Mild Solutions of the Semilinear Initial Value Problem

在文献[2]中利用A是(C_0)类紧半群Γ(t)的无穷小,讨论了算子万程u=Au十f(t,u),u(i)=u。t∈[t_0,T];的mild解的存在性。本文以半序理论及Bochner m-可积为工具,去掉T(t)的紧算子条件,不仅证明了mild解的存在性,且给出解的迭代方法。文献[1]有关结果只是本文A=0的特例。

In this paper we intend to study the existence of the mild solutions of the semilinear initial value problem. where A is the infinitesimal generator of a C_0 semigroup T(t), t≥0, on a partially ordered Banach space E and f:[t,T]×E→E is continuous.The resalt [1] is olly a special case in our study,when A=0.