Previous |  Up |  Next


nonlinear differential system; oscillatory (nonoscillatory) solution
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$.
[1] R. G.  Koplatadze and T. A. Chanturia: On the oscillatory and monotone solutions of the first order differential equations with deviating arguments. J. Diff. Equations 8 (1982), 1463–1465. (Russian)
[2] I.  Foltynska and J. Werbowski: On the oscillatory behaviour of solution of system of differential equation with deviating arguments. Colloquia Math. Soc.  J. B., Qualitative theory of Diff. Eq. Szeged 30 (1979), 243–256. MR 0680596
[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
[4] P.  Marušiak: On the oscillation of nonlinear differential systems with retarded arguments. Math. Slovaca 34 (1984), 73–88. MR 0735938
[5] P. Marušiak and R. Olach: Functional Differential Equations. University of Žilina, EDIS, Žilina, 2000. (Slovak)
Partner of
EuDML logo