FINDING LOGARITHMIC SOLUTIONS TO A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS

The purpose of this work is to study logarithmic solutions of a system of second-order partial differential equations, as well as to establish the conditions of their existence and characterize their properties. Special attention is paid to finding such solutions using the Frobenius-Latysheva method in the vicinity of a regular singular point (0,0). A method has been developed for finding recurrence relations for existing logarithmic solutions when the simple roots of the defining equations differ by integers. A concrete example shows how to construct a logarithmic solution for a homogeneous system of partial differential equations of the second order.