研究多复变广义全纯函数的一个带Haseman位移的非线性边值问题,通过定义相关算子并研究它们的性质,得到了多复变广义全纯函数的Plemelj公式,并将边值问题转化为积分方程问题,利用积分方程方法和Schauder不动点原理证明了解的存在性,得到了解的积分表达式。
A nonlinear boundary value problem with Haseman shift for generalized holomorphic functions of several complex variables is discussed. Firstly, relevant operators are defined and their properties are explored, then Plemelj formula for generalized holomorphic functions of several complex variables is obtained. Secondly, the boundary value problem is transformed into an integral equation problem. Finally, applying the theory of integral equation and the Schauder fixed point theorem, the existence of the solution to the above function is proved and the integral representation of its solution is obtained.