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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (2): 176-188    DOI:
    
Boundary value problems for hypergenic functions
LI Chong, ZHANG Gui-ling, XIE Yong-hong?
College of Mathematics and Information Science, HeBei Normal University, Shijiazhuang 050024, China
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Abstract  Boundary value problems $A(y)\Psi_f^{*+}(y)+B(y)\Psi_f^{*-}(y)=G(y)L(\Psi_f^{*+}(y),\Psi_f^{*-}(y))$ for hypergenic functions in Clifford analysis are mainly discussed. Firstly, the related properties of hypergenic quasi Cauchy integral are considered; secondly, using Schauder fixed point principle the existence of the solution to the nonlinear boundary value problem is proved; finally, the existence and uniqueness of the solution to the linear boundary value problem are proved by virtue of the principle of contraction mapping.

Key words： Clifford analysis      hypergenic function      nonlinear boundary value problem      linear boundary value problem     
Received: 12 December 2016      Published: 01 June 2017
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LI Chong
ZHANG Gui-ling
XIE Yong-hong
Cite this article:

LI Chong, ZHANG Gui-ling, XIE Yong-hong. Boundary value problems for hypergenic functions. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 176-188.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I2/176


hypergenic函数的边值问题

主要研究Clifford分析中hypergenic函数的边值问题$A(y)\Psi_f^{*+}(y)+B(y)\Psi_f^{*-}(y)=G(y)L(\Psi_f^{*+}(y),\Psi_f^{*-}(y))$. 首先讨论hypergenic拟Cauchy型积分的相关性质; 其次利用Schauder不动点原理证明了非线性边值问题解的存在性; 最后利用压缩映射原理证明了线性边值问题解的存在唯一性.

关键词： Clifford分析,  hypergenic函数,  非线性边值问题,  线性边值问题 
[1] YANG He-ju , LI Zun-feng , GUO Bing-chan. $L^p$ intergrability of a higher order Teodorescu operator in Clifford analysis[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 189-197.