MMN-4420
On non-oscillation for two dimensional systems of non-linear ordinary differential equations
Zdeněk Opluštil;
Abstract
The paper studies the non-oscillatory properties of two-dimensional systems of non-linear differential equations u′ = g(t)|v|1 α sgnv,v′ = −p(t)|u|αsgnu, where the functions g: [0,+∞[→ [0,+∞[, p: [0,+∞[→ ℝ are locally integrable and α > 0. We are especially interested in the case of ∫ +∞g(s)ds < +∞. In the paper, new non-oscillation criteria are established. Among others, they generalize well-known results for linear systems as well as second order linear and also half-linear differential equations. The criteria presented complement the results of Hartman-Wintner’s type for the system in question.
Vol. 25 (2024), No. 2, pp. 943-954