Global solvability, stability and oscillation criteria for systems of two first-order pseudo-linear ordinary differential equations

G. A. Grigoryan

Institute of Mathematics of the National Academy of Sciences of the~Republic of Armenia, Yerevan, Armenia

Abstract: The Riccati equation method and other methods are used to establish global solvability, stability, and oscillation criteria for a class of two–dimensional nonlinear systems of ordinary differential equations. The class under study is a generalization of wide classes of second-order nonlinear ordinary differential equations, studied by many authors. The applicability of some of these criteria is illustrated by examples.

Keywords: systems of pseudo-linear equations, Riccati equations, global solvability, van der Pol equation, Duffing equation, Emden–Fowler equation.

MSC: 34D20

Received: 03.09.2025
Revised: 13.10.2025

DOI: 10.4213/tmf11074

 English version: Theoretical and Mathematical Physics, 2026, 226:2, 313–337