| hypergenic函数的边值问题 |
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| 引用本文： | 李冲,张贵玲,谢永红.hypergenic函数的边值问题[J].高校应用数学学报(A辑),2017,32(2). |
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| 作者姓名： | 李冲 张贵玲 谢永红 |
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| 作者单位： | 河北师范大学数学与信息科学学院,河北石家庄,050024 |
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| 基金项目： | 国家自然科学基金，河北省自然科学基金，浙江省自然科学基金，河北师范大学博士基金项目 |
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| 摘 要： | 主要研究Clifford分析中hypergenic函数的边值问题A(y)Ψ*+f(y)+B(y)Ψ*-f(y)=G(y)L(Ψ*+f(y),Ψ*-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.
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| 关 键 词： | Clifford分析 hypergenic函数 非线性边值问题 线性边值问题 |
Boundary value problems for hypergenic functions |
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| LI Chong,ZHANG Gui-ling,XIE Yong-hong.Boundary value problems for hypergenic functions[J].Applied Mathematics A Journal of Chinese Universities,2017,32(2). |
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| Authors: | LI Chong ZHANG Gui-ling XIE Yong-hong |
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| Abstract: | Boundary value problems A(y)Ψ?+f (y)+B(y)Ψ?-f (y) = G(y)L(Ψ?+f (y),Ψ?-f (y)) for hypergenic functions in Clifford analysis are mainly discussed. Firstly, the related properties of hyper-genic 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. |
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| Keywords: | Clifford analysis hypergenic function nonlinear boundary value problem linear boundary value problem |
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