Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations

For the system of non-linear equations u′=g(t)|v|1/αsgnv,v′=−p(t)|u|αsgnu with α>0α>0 and locally integrable functions g:[0,+∞[→[0,+∞[g:[0,+∞[→[0,+∞[, p:[0,+∞[→Rp:[0,+∞[→R, new oscillation criteria are given in both cases ∫0+∞g(s)ds=+∞ and ∫0+∞g(s)ds<+∞. 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)ds<+∞, does not require the assumption p≥0p≥0 appearing in the existing literature.