The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

Abstract

In this article, we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order

$w_{z\bar z} = F(z,w,w_z ,\bar w_z ,w_{zz} ,\bar w_{zz} ) + G(z,w,w_z ,\bar w_z )inD$

((0.1))

, with the boundary conditions

in a multiply connected unbounded domain D. The above boundary value problem will be called Problem P. Under certain conditions, by using the priori estimates of solutions and Leray-Schauder fixed point theorem, we can obtain some results of the solvability for the above boundary value problem (0.1) and (0.2).