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The mixed problem for nonlinear elliptic complex equations in multiply-connected domains

Abstract In this article, we discuss the mixed boundary value problem for nonlinear uniformly elliptic complex equation of second order(1) with the boundary conditions(2) in a multiply-connected domain . If the complex equation (0.1) satisfies the conditions similar to Condition C in (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5) below, then we can obtain some solvability results for the above boundary value problem (0.1) and (0.2). But, we need to propose a modified well-posedness of the above boundary value problem, and first discuss its solvability, in which the fixed-point theorem for proving its solvability is applied.