【作者】 李浩；

【导师】 张传义；

【作者基本信息】 哈尔滨工业大学 ， 基础数学， 2006， 硕士

【摘要】 Hille和Yosida首先给出了C₀半群的生成元定理,但是人们对于非线性算子半群的研究进展的相当缓慢。本文给出了一种新的非线性算子半群,非线性Lipschitz-α算子半群。这种算子半群是在非线性算子半群的基础上提出的,是对非线性Lipschitz算子半群的进一步扩展,使它的范围更加扩大了。本文仔细研究了这种半群,并给出了它的一种生成元的存在性定理。本文共分三章,主要内容如下:在第一章回顾了算子半群的发展历程和非线性算子半群的研究以及发展现状,接着介绍了研究非线性Lipschitz-α算子半群的意义。在第二章介绍了赋范空间,算子理论知识,算子半群的有关知识。在第三章中给出了关于非线性Lipschitz-α算子半群的生成元存在性定理。更多还原

【Abstract】 Hille and Yosida proved the generation theorem of C₀ semigroups firstly, but the course of study of a nonlinear semigroups is very slow. This paper is concerned with the problem of a nonlinear semigroup of Lipschitz-αoperator, based on the nonlinear semigroup of Lipschitz operator. This new semigroup extende the nonlinear semigroup of Lipschitz operator. In this paper, new theorems of the generation of the nonlinear semigroup of Lipschhitz-αoperator are established.This paper consists of three chapters. The main contents are the following:In the first chapter, we recall the development of the semigroups. Then we introduce the meaning of doing research on the nonlinear semigroups of Lipschitz -αoperator.In the second chapter, we present some mathematical preliminaries. These include the theorems in normed spaces, operator theory and operator semigroup. In the third chapter, we established the new theory of the nonlinear semigroup of the Lipschitz-αoperator.更多还原