中文摘要：

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.

英文摘要：

This paper discusses a nonlinear boundary value problem with a shift for gen- eralized 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.