摘要
从应用问题的需要出发,给出了一类新的算子-凸幂凝聚算子的定义,推广了凝聚算子的概念,并证明了这类新算子的不动点定理,从而推广了著名的Schauder不动点定理和Sadovskii不动点定理.作为应用,获得了Banach空间中一类具有非紧半群的半线性发展方程初值问题整体mild解和正mild解的存在性.
We give the definition of a kind of new operator-convex-power condensing operator for the need of applied questions and generalize the definition of condensing operator. The fixed point theorem of this kind of new operator is proved. This generalizes the famous Schauder fixed point theorem and Sadovskii fixed point theorem. As applications, the existence of global mild solutions and positive mild solutions of initial value problem for a class of semilinear evolution equations with noncompact semigroup in Banach spaces is obtained.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2005年第3期439-446,共8页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(10371066)山东省自然科学基金资助项目(Y2003A01)
关键词
凸幂凝聚算子
不动点定理
抽象发展方程
Convex-power condensing operator
Fixed point theorem
Abstract evolution equation