IRREGULAR OBLIQUE DERIVATIVE PROBLEMS FOR SECOND-ORDER NONLINEAR ELLIPTIC EQUATIONS ON INFINITE DOMAINS

In this article, we study irregular oblique derivative boundary-value problems for nonlinear elliptic equations of second order in an infinite domain. We first provide the formulation of the above boundary-value problem and obtain a representation theorem. Then we give a priori estimates of solutions by using the reduction to absurdity and the uniqueness of solutions. Finally by the above estimates and the Leray-Schauder theorem, the existence of solutions is proved.