Geodesic
Oscillation of nonlinear differential systems with retarded arguments
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 255-262
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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$.
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$.
Classification : 34K11, 34K15, 34K40
Keywords: nonlinear differential system; oscillatory (nonoscillatory) solution 
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Bačová, Beatrix; Dorociaková, Božena. Oscillation of nonlinear differential systems with retarded arguments. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 255-262. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a18/

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