Oscillation criteria for two-dimensional system of non-linear ordinary differential equations

New oscillation criteria are established for the system of non-linear equations u' = g (t) vertical bar v vertical bar(1/alpha)sgn v, v' = p (t) vertical bar u vertical bar(alpha) sgn u, where alpha > 0, g : [0, + infinity[ -> [0, + infinity[, and p : [0, + infinity[ -> R are locally integrable functions. Moreover, we assume that the coefficient g is non-integrable on [0, + infinity]. Among others, presented oscillatory criteria generalize well-known results of E. Hille and Z. Nehari and complement analogy of Hartman-Wintner theorem for the considered system.