多复变双解析函数中的一个非线性边值问题

研究了二元复变双解析函数的一个非线性边值问题。首先给出了二元复变双解析函数的定义,讨论了二元双解析函数的Cauchy积分定理和Cauchy积分公式;其次给出了二元复变双解析函数的Cauchy-Fredholm型积分和P lem elj公式;最后,在此基础上提出了一个非线性边值问题,并将此边值问题转化为积分方程组问题,然后利用积分方程方法和Schauder不动点定理证明解的存在性,并获得解的积分表达式

A Nonlinear Boundary Value Problem in Bianalytic Analytic Functions of Several Complex Variable

In this paper,we study a nonlinear boundary value problem in bianalytic functions of double complex variables.Firstly,we give the definition of bianalytic functions of double complex variables and discuss the Cauchy integral theorem and the Cauchy integral formula in the bianalytic functions of double complex variables.Secondly,we give the Cauchy-Fredholm type integral and the Plemelj formula in bianalytic functions of double complex variables.Finally,we pose a nonlinear boundary value problem in the questions mentioned above,Moreover,we transform the boundary value problem into an integral equation system problem.Applying the method of integral equations and Schauder fixed-point theorem,we prove existence of solution and get integral representations of solution: