Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations. (June 2015) - Dosoudilová, Monika; Lomtatidze, Alexander; Šremr, Jiří
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.