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Clifford分析中多个未知函数向量的非线性边值问题
引用本文:黄沙,焦红兵,乔玉英,陈振国.Clifford分析中多个未知函数向量的非线性边值问题[J].数学学报,1998,41(6):0-1192.
作者姓名:黄沙  焦红兵  乔玉英  陈振国
作者单位:河北师范大学数学系!石家庄,050016,河北师范大学数学系!石家庄,050016,河北师范大学数学系!石家庄,050016,河北师范大学数学系!石家庄,050016
基金项目:国家自然科学基金!19771068,河北省自然科学基金,河北省教委自然科学基金
摘    要:设fi(x),1≤i≤p为取值在实2n-1维代数An(R)上的函数.我们称F(x)=(f1,f2,...,fp)为函数向量,而fi,1≤i≤p为向量F的分量,本文借助于向量值分析的思想,利用积分方程方法、Shauder不动点原理和压缩映射原理研究多个未知函数的函数向量F带位移又带共轭值的四元素非线性过值问题解的存在性和相应线性边值问题解的存在唯一性.

关 键 词:Clifford分析  奇异积分方程  向量  位移  非线性边值问题

Nonlinear Boundary Value Problems for Several Unknown Functions Vector in Clifford Analysis
Huang Sha, Jiao Hongbing, Qiao Yuying, Chen Zhenguo.Nonlinear Boundary Value Problems for Several Unknown Functions Vector in Clifford Analysis[J].Acta Mathematica Sinica,1998,41(6):0-1192.
Authors:Huang Sha  Jiao Hongbing  Qiao Yuying  Chen Zhenguo
Institution:Huang Sha; Jiao Hongbing; Qiao Yuying; Chen Zhenguo (Department of Mathematics, Hebei Teacher 's University, Shi Jiazhuang 050016, China)
Abstract:Letting fi(x), i = 1,..., p be function with value in a Clifford algebra An(R). we call F(x) = (f1, f2,.... fp) function vector, where f1, f2,..., fp are vector components for F(x). In this paper, by thinking of the vector-valued analysis, we discuss a four elements nonlinear boundary value problem for several unknown functions vector with shifts and conjugate and a corresponding linear boundary problem.Applying the method of integral equations and Shauder fixed-point theorem and contract mapping theorem, we prove the existence of solution for the nonlinear problem and the existence and uniqueness for the linear problem.
Keywords:Clifford analysis  Singular integral equations  Vector  Shifts  Nonlinear boundary value problem
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