The behavior of solutions of the systems of two first order linear ordinary differential equations

Abstract

The Riccati equation method is used for study the behavior of solutions of the systems of two linear first order ordinary differential equations. All types of oscillation and regularity of these system are revealed. A generalization of Leighton's theorem is obtained. Three new principles for the second order linear differential equations are derived. Stability and non conjugation criteria are proved for the mentioned systems, as well as estimates are obtained for the solutions of the last ones.