We consider partial differential equations of second order of formally-hyperboiic or elliptic type which possess differential operators after K. W. Bauer for the representation of its solutions. These operators act on the space of holomorphic functions. Relations between the solutions and the functions generating them are derived. With this it is possible to give general representation theorems for solutions defined in the neighbourhood of isolated singularities. Doing so we discuss unique solutions as well as branched ones.