Some nonlinear boundary value problems for nonlinear elliptic equations of second order in the plane

Abstract

In this paper, we discuss some nonlinear Poincare boundary value problems for nonlinear uniformly elliptic equations of second order in a multiply connected domain by using the methods of complex functions. At first we propose some modified boundary value problems for nonlinear elliptic systems of first order and give a priori estimates of solutions for the modified problems. Afterwards applying the above results, the continuity method and Schauder fixed-point theorem, we prove that the above nonlinear Poincare problems with some conditions has a solution.