On the absolutely continuous spectrum of a vector-matrix Dirac system

Abstract

A Dirac system is considered which has a matrix-valued long-range, short-range and oscillatory potentials. The system has one singular endpoint at infinity. Additional conditions on the potential are given which guarantee particular asymptotic behaviour of an energy functional associated with a certain set of solutions. This asymptotic behaviour guarantees the existence of a purely absolutely continuous spectrum outside a gap containing the origin.