The Dirichlet type problem for a class of nonlinear Carleman — Vekua equations with a singular point.

Abstract

In this paper we obtain sufficient condition for existence of continuou s solutions in the infinite angular domain Dirichlet type problem for a class of the first order elliptic systems of nonlinear partial differential equations on the plane with a sin gular point which occurs in the theory of infinitesimal deformations of surfaces of positive curvature with a flat point of general structure. For the reduction of this problem to a nonlinear integral equation we use the formula for finding of general solution of appropriate fi rst order partial differential elliptic system of linear equations on the plane with a singular po int which was obtained by A. Tungatarov. Schauder fixed point principle was used to prove th e existence of continuous solutions of the Dirichlet problem.