Asymptotic expansions for bounded solutions to semilinear Fuchsian equations

Abstract

It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptotic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schulze's notion of asymptotic type for conormal asymptotic expansions near a conical point is refined. This in turn allows to perform explicit computations on asymptotic types – modulo the resolution of the spectral problem for determining the singular exponents in the asymptotic expansions.