Previous |  Up |  Next


Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations \[ (-1)^{m+1}\frac{d^my_i(t)}{dt^m} + \sum ^n_{j=1} q_{ij} y_j(t-h_{jj})=0, \quad m \ge 1, \ i=1,2,\ldots ,n, \] to be oscillatory, where $q_{ij} \varepsilon (-\infty ,\infty )$, $h_{jj} \in (0,\infty )$, $i,j = 1,2,\ldots ,n$. Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations \[ (-1)^{m+1} \frac{d^m}{dt^m} (y_i(t)+cy_i(t-g)) + \sum ^n_{j=1} q_{ij} y_j (t-h)=0, \] where $c$, $g$ and $h$ are real constants and $i=1,2,\ldots ,n$.
[1] K. Gopalsamy: Oscillatory properties of systems of first order linear delay differential inequalities. Pacific J. Math. 128 (1987), 299–305. DOI 10.2140/pjm.1987.128.299 | MR 0888519 | Zbl 0634.34054
[2] K. Gopalsamy and G. Ladas: Oscillations of delay differential equations. J. Austral Math. Soc. Ser. B. 32 (1991), 377–381. DOI 10.1017/S0334270000008493 | MR 1097110
[3] I. Györi and G. Ladas: Oscillation Theory of Delay Differential Equations with Applications. Oxford University Press, Oxford, 1991. MR 1168471
[4] I. T. Kiguradze: On the oscillation of solutions of the equation ${}^mu/t^m+a(t) |u|^n u=0$. Mat. Sb. 65 (1964), 172–187. (Russian) MR 0173060 | Zbl 0135.14302
[5] G. Ladas and I. P. Stavroulakis: On delay differential inequalities of higher order. Canad. Math. Bull. 25 (1982), 348–354. DOI 10.4153/CMB-1982-049-8 | MR 0668953
[6] Ch. G. Philos: On the existence of the nonoscillatory solutions tending to zero at $\infty $ for differential equations with positive delays. Arch. Math. 36 (1981), 168–178. DOI 10.1007/BF01223686 | MR 0619435
Partner of
EuDML logo