On non-oscillation for two dimensional systems of non-linear ordinary differential equations

Opluštil, Zdeněk (2024) On non-oscillation for two dimensional systems of non-linear ordinary differential equations. Miskolc Mathematical Notes, 25 (2). pp. 943-954. ISSN 1787-2413

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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.

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