Generalized power series solutions to linear partial differential equations

Let and , where is an effective field and and are given a suitable asymptotic ordering . Consider the mapping , where L1,…,Ll Θ. For , it is natural to ask how to solve the system Lf=g. In this paper, we will effectively characterize and show how to compute a so called distinguished right inverse of L. We will also characterize the solution space of the homogeneous equation Lh=0.