Asymptotic Solutions of Second Order Equations with Holomorphic Coefficients with Degeneracies and Laplaces Equations on a Manifold with a Cuspidal Singularity

Abstract

In this paper, we construct the asymptotics for second order linear differential equations with higher-order singularity for the case where the principle symbol has multiple roots. In addition, we solve the problem of constructing asymptotic solutions of Laplace’s equation on a manifold with a second order cuspidal singularity.