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.
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 axe 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.