On the Weyl--type solutions of differential systems with a singularity. Case of discontinuous potential

TL;DR

This paper investigates Weyl-type solutions for a differential system with a singularity and an integrable potential, focusing on the case where the potential is discontinuous, to understand their properties and behavior.

Contribution

It introduces a new analysis of Weyl-type solutions for differential systems with singularities and discontinuous potentials, expanding existing theoretical frameworks.

Findings

Characterization of Weyl-type solutions in the presence of singularities.

Conditions under which solutions exist and are unique.

Insights into the impact of discontinuous potentials on solution behavior.

Abstract

We study the Weyl-type solutions of the differential system with a singularity $y'-x^{-1}Ay-q(x)y=\rho By$ in the case of integrable potential $q(\cdot)$.