Oscillation and Nonoscillation for Two-dimensional Nonlinear Systems of Ordinary Differential Equations

For the two-dimensional nonlinear system u ' = a(t)vertical bar v vertical bar(1/alpha) sgn v, v ' = -b(t)vertical bar u vertical bar(alpha) sgn u with alpha > 0, a, b is an element of C[t(0), infinity), a(t) >= 0 (t >= t(0)), new oscillation criteria and nonoscillation criteria are given in both cases integral(infinity)(t0) a(s) ds = infinity and integral(infinity)(t0) a(s) ds < infinity. One of the main results is an analogue of the Hartman-Wintner oscillation theorem. Our results generalize Li and Yeh's results for second order half-linear scalar equations.