Oscillation of solutions of a system of differential equations

Abstract

The system

$$u_1^\prime = a_1 (t)|u_2 |^{\lambda _1 } sign u_2^\prime = - a_2 (t)|u_1 |^{\lambda _2 } sign u_1 ,$$

is considered, where the functionsa _i: [0, +∞)→R (i=1, 2) are locally summable, λ_i>0 (i=1, 2) and λ₁·λ₂=1. Sufficient conditions are obtained for all solutions of system (1) to be oscillating. Furthermore, functionsa _i(t) (i=1, 2) are, generally speaking, not assumed to be nonnegative.