Behavior at infinity of solutions of second-order nonlinear equations of a particular class

Abstract

Let Ω be an arbitrary, possibly unbounded, open subset of ℝn, and letL be an elliptic operator of the form $$L = \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial x_i }}\left( {a_{ij} (x)\frac{\partial }{{\partial x_j }}} \right)} $$ . The behavior at infinity of the solutions of the equationLu=ƒ(¦u¦)signu in Ω is studied, whereƒ is a measurable function. In particular, given certain conditions at infinity, the uniqueness theorem for the solution of the first boundary value problem is proved.