On a boundary value problem for semilinear elliptic system of second order in the plane

Abstract

A well-posed boundary value problem for a semilinear elliptic system of second order in the plane is solved. The principal part of the equation is one of the canonical forms of second order partial differential equations with constant coefficients in the plane. The parameter λ corresponds to respectively strongly and non-strongly elliptic equations for λ > 0 and λ < 0.