Asymptotic Dirichlet problem for the Schrödinger operator on negatively curved manifolds

Abstract

In this paper, we consider the asymptotic Dirichlet problem for the Schrödinger operator on a Cartan-Hadamard manifold with suitably pinched curvature. With potentials satisfying a certain decay rate condition, we give the solvability of the asymptotic Dirichlet problem for the Schrödinger operator. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.