CONSTRUCTION OF NORMAL SOLUTIONS FOR INHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULARITIES

The problem of constructing a normal solution to inhomogeneous systems of second-order partial differential equations using the Frobenus-Latysheva method in the neighborhood of an irregular singular point is considered. The compatibility conditions for the considered inhomogeneous system of partial differential equations are shown and an algorithm for constructing normal solutions in the vicinity of a point at infinity is created. A theorem on the structure of the general solution of inhomogeneous systems of second-order partial differential equations is proved and a “resonance” system is studied, which arises if the particular solution of the corresponding homogeneous system coincides on the right side of the inhomogeneous system. A specific example shows how to construct a particular solution to a non-homogeneous system of partial differential equations.