Oscillations of certain functional differential equations

Grace, Said R.. "Oscillations of certain functional differential equations." Czechoslovak Mathematical Journal 49.1 (1999): 45-52. <http://eudml.org/doc/30463>.

@article{Grace1999,
abstract = {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 $i=1,2,\ldots ,n$.},
author = {Grace, Said R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear system of delay equations; neutral equation; bounded solution; oscillation},
language = {eng},
number = {1},
pages = {45-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillations of certain functional differential equations},
url = {http://eudml.org/doc/30463},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Grace, Said R.
TI - Oscillations of certain functional differential equations
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 1
SP - 45
EP - 52
AB - 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 $i=1,2,\ldots ,n$.
LA - eng
KW - linear system of delay equations; neutral equation; bounded solution; oscillation
UR - http://eudml.org/doc/30463
ER -