广义超正则函数的一个带位移的非线性边值问题
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摘要
讨论了一个广义超正则函数的带位移的非线性边值问题.首先将这个广义超正则函数分解为两个积分算子的和并讨论了相关奇异积分算子的性质,然后利用超正则函数的Plemelj公式和Schauder不动点定理证明了这个广义超正则函数的带位移的非线性边值问题的解的存在性和唯一性.
This paper discusses a nonlinear boundary value problem with a shift for generalized hypermonogenic function.Firstly we decompose the generalized hypermonogenic function into integral operators and discuss the properties of some integral operators.Then by the Plemelj formula for hypermonogenic functions and Schauder fixed point theorem,we prove the existence and uniqueness of the solution to the nonlinear boundary value problem with a shift for generalized hypermonogenic function.
This paper discusses a nonlinear boundary value problem with a shift for generalized hypermonogenic function.Firstly we decompose the generalized hypermonogenic function into integral operators and discuss the properties of some integral operators.Then by the Plemelj formula for hypermonogenic functions and Schauder fixed point theorem,we prove the existence and uniqueness of the solution to the nonlinear boundary value problem with a shift for generalized hypermonogenic function.
引文
[1]Wen G C.Clifford analysis and elliptic system,Hyperbolic systems of first order equations[C]//Singapore:World Scientific,1991:230-237.
[2]Huang S,Qiao Y Y,and Wen Guochun.Real and Complex Clifford Analysis[M].Springer,USA,2006.
[3]Qiao Y Y.A boundary value problem for hypermonogenic functions in Clifford analysis[J].Science in China Series(A).2005,48:324-333.
[4]Zhang Z X.Some properties of operators in Clifford analysis[J].Complex var Elliptic Eq,2007,52(6):455-473.
[5]张忠祥,杜金元.关于Clifford分析中的某些Riemanns边值问题与奇异积分方程[J].数学年刊.2001,22A(4):421-426.
[6]Qiao Y Y,Ryan J,Bernstein S,Eriksson S L.Function theory for Laplace and Dirac hodge operators on hyperbolic space[J].Journal D Analyse Mathematique,2006,98:43-63.
[7]谢永红,杨贺菊.广义双正则函数向量的非线性边值问题[J].数学物理学报,2003,25(1):291-295.
[8]杨贺菊,李海萍.双曲空间中Laplace-Beltrami方程的一个带位移的边值问题[J].数学的实践与认识,2012,42(16):253-257.
[9]杨贺菊,李海萍.Clifford分析中广义超正则函数的一个非线性边值问题[J].数学的实践与认识,2014,44(8):241-246.
[10]Eriksson S L.Integral Formulas for Hypermonogenic Functions[J].Bull Belg Math Soc,2004,11:705-718.
[11]Gilbert R P,Buchanan J L.First order elliptic systems A functions theoretic approach Academic press[M].New York,1983.
[2]Huang S,Qiao Y Y,and Wen Guochun.Real and Complex Clifford Analysis[M].Springer,USA,2006.
[3]Qiao Y Y.A boundary value problem for hypermonogenic functions in Clifford analysis[J].Science in China Series(A).2005,48:324-333.
[4]Zhang Z X.Some properties of operators in Clifford analysis[J].Complex var Elliptic Eq,2007,52(6):455-473.
[5]张忠祥,杜金元.关于Clifford分析中的某些Riemanns边值问题与奇异积分方程[J].数学年刊.2001,22A(4):421-426.
[6]Qiao Y Y,Ryan J,Bernstein S,Eriksson S L.Function theory for Laplace and Dirac hodge operators on hyperbolic space[J].Journal D Analyse Mathematique,2006,98:43-63.
[7]谢永红,杨贺菊.广义双正则函数向量的非线性边值问题[J].数学物理学报,2003,25(1):291-295.
[8]杨贺菊,李海萍.双曲空间中Laplace-Beltrami方程的一个带位移的边值问题[J].数学的实践与认识,2012,42(16):253-257.
[9]杨贺菊,李海萍.Clifford分析中广义超正则函数的一个非线性边值问题[J].数学的实践与认识,2014,44(8):241-246.
[10]Eriksson S L.Integral Formulas for Hypermonogenic Functions[J].Bull Belg Math Soc,2004,11:705-718.
[11]Gilbert R P,Buchanan J L.First order elliptic systems A functions theoretic approach Academic press[M].New York,1983.