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抽象半线性发展方程初值问题解的存在性
引用本文:李永祥.抽象半线性发展方程初值问题解的存在性[J].数学学报,2005,48(6):1089-1094.
作者姓名:李永祥
作者单位:西北师范大学数学与信息科学学院 兰州
基金项目:甘肃省自然科学基金(ZS031-A25-003-Z)及NWNU-KJCXGC-212基金资助项目
摘    要:本文研究Banach空间E中具有非紧半群的半线性发展方程初值问题u′(t)+Au(t)=f(t,u(t)),t≥0;u(0)=x_0解的存在性,其中-A为E中等度连续C_0-半群的生成元,f:0,∞)×E→E连续。在f满足较弱的非紧性测度条件下,获得了该问题饱和mild解的存在性。特别,当E为有序弱序列完备Banach空间时,我们获得了一个不需要非紧性测度条件的便于应用的存在性结果。

关 键 词:抽象发展方程  C_0-半群  存在性
文章编号:0583-1431(2005)06-1089-06
收稿时间:2003-02-19
修稿时间:2003-02-192004-10-20

Existence of Solutions of Initial Value Problems for Abstract Semilinear Evolution Equations
Yong Xiang LI College of Mathematics and Information Seience,Northwest Normal University,Lanzhou ,P. R. China.Existence of Solutions of Initial Value Problems for Abstract Semilinear Evolution Equations[J].Acta Mathematica Sinica,2005,48(6):1089-1094.
Authors:Yong Xiang LI College of Mathematics and Information Seience  Northwest Normal University  Lanzhou  P R China
Institution:Yong Xiang LI College of Mathematics and Information Seience, Northwest Normal University, Lanzhou 730070, P. R. China
Abstract:This paper discusses the existence of solutions of initial value problem for semilinear evolution equation with noncompact semigroup u'(t)+Au(t)=f(t, u(t)), t≥0; u(0)=x_0 in a Banach space E, where -A is the infinitesimal generator of an equicontinuous C_0-semigroup, and f: 0, ∞)×E→E is continuous. In the case where f satisfies a weaker noncompactness measure condition, the existence results of saturated mild solutions are obtained. Particularly, an existence result without using noncompactness measure condition is present in ordereded and weakly sequentially complete Banach spaces. This result is very convenient for application.
Keywords:Abstract evolution equation  C0-semigroup  Existence
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