关键词: 多复变广义全纯函数, Haseman位移, 非线性边值问题

Abstract:

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.

Key words: generalized holomorphic function of several complex variables, Haseman shift, nonlinear boundary value problem