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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
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