UNIQUENESS OF SOLUTIONS OF A CERTAIN NONLINEAR ELLIPTIC EQUATION ON RIEMANNIAN MANIFOLDS

Abstract

In this paper, we prove that if every bounded A-harmonic function on a complete Riemannian manifold M is asymptotically constant at infinity of p-nonparabolic ends of M, then each bounded A-harmonic function is uniquely determined by the values at infinity of p-nonparabolic ends of M, where A is a nonlinear elliptic operator of type p on M. Furthermore, in this case, every bounded A-harmonic function on M has finite energy.