Geodesic
Oscillation of solutions of a system of differential equations
Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 401-404 
J. D. Mirzov. Oscillation of solutions of a system of differential equations. Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 401-404. http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a7/
@article{MZM_1978_23_3_a7,
     author = {J. D. Mirzov},
     title = {Oscillation of solutions of a~system of differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--404},
     year = {1978},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The system $$ u'_1=a_1(t)|u_2|^{\lambda_1}\operatorname{sign}u_2,\qquad u'_2=-a_2(t)|u_1|^{\lambda_2}\operatorname{sign}u_1,\eqno(1) $$ is considered, where the functions $a_i:[0,+\infty)\to\mathbf R$ $(i=1,2)$ are locally summable, $\lambda_i>0$ $(i=1,2)$ and $\lambda_1\cdot\lambda_2=1$. Sufficient conditions are obtained for all solutions of system (1) to be oscillating. Furthermore, functions $a_i(t)$ $(i=1,2)$ are, generally speaking, not assumed to be nonnegative.