Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations. (June 2015)

• Record Type: Journal Article
• Authors: Dosoudilová, Monika; Lomtatidze, Alexander; Šremr, Jiří
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 57
• Page End: 75
• Publication Date: 2015-06
• Subjects: 34C10; Half-linear system -- Kamenev theorem -- Hartman–Wintner theorem -- Oscillation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.02.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For the system of non-linear equations u ′ = g ( t ) | v | 1 / α sgn v, v ′ = − p ( t ) | u | α sgn u with α > 0 and locally integrable functions g : [ 0, + ∞ [ → [ 0, + ∞ [, p : [ 0, + ∞ [ → R, new oscillation criteria are given in both cases ∫ 0 + ∞ g ( s ) d s = + ∞ and ∫ 0 + ∞ g ( s ) d s < + ∞ . As a consequence of the main results we derive, among others, a Hartman–Wintner type theorem for the system considered which, in the case ∫ 0 + ∞ g ( s ) d s < + ∞, does not require the assumption p ≥ 0 appearing in the existing literature.