## On the principal and nonprincipal solutions of a nonlinear system.(Russian. English summary)Zbl 0735.34029

Summary: The behavior at $$+\infty$$ of the principal and nonprincipal solutions of the system $u'_ i=(-1)^{i-1}a_ i(t)| u_{3- i}|^{\lambda_ i}\text{sign} u_{3-i}\qquad (i=1,2)$ is studied. By means of the obtained results sufficient conditions for oscillation of solutions are established.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations