Integral Representations of Solutions to an Overdetermined System with Two Internal Singular Lines

Abstract

In this article, integral representations of solutions are obtained for an overdetermined system of second-order differential equations with two internal singular lines, under a specified relation between the coefficients of the first and second equations. The solution manifold is represented through one arbitrary constant by applying a methodology developed for overdetermined systems with singular and supersingular coefficients. Two cases are considered, depending on which equation is taken as the principal equation. The corresponding solution representations are derived, and several properties of the solutions are established. In addition, two initial value problems are formulated and uniqueness of their solutions is proved under the stated conditions. The results provide integral representations and solvability criteria for a class of overdetermined differential systems with two internal singular lines, contributing to the analysis of differential equations with singular structures.