概率赋范空间中的非线性半群与微分包含<sup>*</sup>

张石生; 陈玉清

概率赋范空间中的非线性半群与微分包含^*

四川大学数学系, 成都 610064

基金项目: * 国家自然科学基金

详细信息

中图分类号: O177
计量
- 文章访问数: 2257
- HTML全文浏览量: 226
- PDF下载量: 525
- 被引次数: 0
出版历程
- 收稿日期: 1996-12-30
- 修回日期: 1998-02-20
- 刊出日期: 1998-09-15

Nonlinear Semigroups and Differential Inclusions in Probabilistic Normed Spaces

Department of Mathematics, Sichuan University, Chengdu, 610064, P.R. China

摘要

摘要: 本文的目的是在概率赋范空间中引入和研究非线性压缩半群,并对增生映象建立Crandal-Ligget指数公式.作为应用,我们将应用这些结果研究概率赋范空间中一类具增生映象的微分包含的Cauchy问题解的存在性.
- 非线性压缩半群 /
- 概率赋范空间 /
- Crandall-Liggett指数公式 /
- 半内积 /
- 增生映象
Abstract: The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces.As applications,these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
- semigroup of nonlinear contractions /
- probabilistic normed space /
- Crandall-Liggett’s exponential formula /
- semi-inner produet /
- accretive mappings

HTML全文

参考文献(16)

[1]	V.Barbu,Nonlinear Semigroups and Differential Equations in Banach Spaces,Noordhoff International Publishing House (1976).
[2]	H.Brezis and A.Pazy,Semigroups of nonlinear contractions on convex sets,J.Funct.Anal.,(1970),367-383.
[3]	F.E.Browder,Nonlinear mappings of nonexpansive and accretive type in Banach spaces,Bull.Amer.Math.Soc.,73 (1967),875-882.
[4]	F.E.Browder,Nonlinear operators and nonlinear equations of evolution in Banach spaces,Proc.Symp.Pure.Math.,18,Part 2 (1976).
[5]	张石生、陈玉清,概率赋范空间中具增生映象的方程解的存在性,应用数学和力学,11(9) (1990),771-778.
[6]	S.S.Chang,Y.J.Cho and S.M.Kang,Probabilistic Metric Spaces and Nonlinear Operator Theory,Sichuan University Press (1994).
[7]	M.G.Crandall and T.Liggett,Generations of semi-groups of nonlinear transformations on general Banach spaces,Amer.J.Math.,93 (1971),265-298.
[8]	M.G.Crandall and A.Pazy,Semigroups of nonlinear contractions and dissipative sets,J.Funct.Anal.,3 (1969),37-418
[9]	K.S.Ha,K.Y.Shin and Y.J.Cho,Accretive operators in probabilistic normed spaces,Bull.Korean Math.Soc.,31(1) (1994),45-54.
[10]	T.Kato,Nonlinear semigroups and evolution equations,J.Math.Soc.Japan,1(1967),505-520.
[11]	T.Kato,Accretive operators and nonlinear evolution equations in Banach spaces,Proc.Symp.Pure Math.,1(1970),138-161.
[12]	Y.Komura,Nonlinear semigroups in Hibert spaces,J.Math.Soc.Japan,1(1967),493-507.
[13]	V.Lakshmikantham and S.Leela,Nonlinear Differ ential Equations in Abstract Spaces,Pergamon Press (1981).
[14]	G.Lumer,Semiinner product spaces,Trans.Amer.Math.Soc.,100 (1961),29-43.
[15]	W.Rudin,Functional Analysis,McGraw-Hill Book Company (1973).
[16]	B.Schweizer and A.Sklar,Probabilistic Metric Spaces,North-Holland (1983).