Geodesic
Oscillations of certain functional differential equations
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 45-52 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $i=1,2,\ldots ,n$.
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 $i=1,2,\ldots ,n$.
Classification : 34K11, 34K40 
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     author = {Grace, S. R.},
     title = {Oscillations of certain functional differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {45--52},
     year = {1999},
     volume = {49},
     number = {1},
     mrnumber = {1676690},
     zbl = {0955.34051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999_49_1_a4/}
}
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Grace, S. R. Oscillations of certain functional differential equations. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 1, pp. 45-52. http://geodesic.mathdoc.fr/item/CMJ_1999_49_1_a4/

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