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凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用
引用本文:孙经先,张晓燕.凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用[J].数学学报,2005,48(3):439-446.
作者姓名:孙经先  张晓燕
作者单位:[1]徐州师范大学数学系,徐州221116 [2]山东大学数学与系统科学学院,济南250100
基金项目: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)
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.

关 键 词:凸幂凝聚算子  不动点定理  抽象发展方程

The Fixed Point Theorem of Convex-Power Condensing Operator and Applications to Abstract Semilinear Evolution Equations
Jing Xian SUN.The Fixed Point Theorem of Convex-Power Condensing Operator and Applications to Abstract Semilinear Evolution Equations[J].Acta Mathematica Sinica,2005,48(3):439-446.
Authors:Jing Xian SUN
Institution:Jing Xian SUN Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, P. R. China Xiao Yan ZHANG School of Mathematics and Systems Science, Shandong University, Jincn 250100, P. R. China
Abstract: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.
Keywords:Convex-power condensing operator  Fixed point theorem  Abstract evolution equation
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