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Keywords:
nonlinear differential system; oscillatory (nonoscillatory) solution
nonlinear differential system; oscillatory (nonoscillatory) solution
Summary:
In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form \[ y^{\prime }_i(t)-p_i(t)y_{i+1}(t)=0, \quad i=1,2,\dots , n-2, y^{\prime }_{n-1}(t)-p_{n-1}(t)|y_n(h_n(t))|^\alpha \mathop {\mathrm sgn}[y_n(h_n(t))]=0, y^{\prime }_n(t) \mathop {\mathrm sgn}[y_1(h_1(t))]+p_n(t)|y_1(h_1(t))|^\beta \, \le 0, \] where $ n\ge 3 $ is odd, $ \alpha >0$, $ \beta >0$.
References:
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[3] Y. Kitamura and T. Kusano: On the oscillation of a class of nonlinear differential systems with deviating argument. J. Math. Annal Appl. 66 (1978), 20–36. MR 0513483
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[5] P. Marušiak and R. Olach: Functional Differential Equations. University of Žilina, EDIS, Žilina, 2000. (Slovak)
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