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This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.

General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains