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Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations. (English) Zbl 1336.34053
The authors derive new oscillation criteria for the nonlinear system
$u'=g(t)\,|v|^{1/\alpha}{\text{sgn}}v, \quad v'=-p(t)\,|u|^\alpha{\text{sgn}}u, \tag{*}$ where $$\alpha>0$$, the coefficients $$g$$ and $$p$$ are locally integrable on $$[0,\infty)$$, and $$g(t)\geq0$$ with $$\int_0^\infty g(t)\,dt=\infty$$ or $$\int_0^\infty g(t)\,dt<\infty$$. No sign condition on $$p(t)$$ is imposed. The authors establish new Kamenev and Hartman-Wintner type criteria for system ($$*$$), which extend known results in the literature. The proofs are based on a sophisticated analysis of inequalities involving the (assumed) nonoscillatory solutions of ($$*$$).

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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##### References:
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