Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

Rath, R.N., Panda, K.C., and Rath, S.K.. "Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator." Archivum Mathematicum 058.2 (2022): 65-84. <http://eudml.org/doc/298324>.

@article{Rath2022,
abstract = {In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation \[ \big (y(t)- \sum \_\{i=1\}^k p\_i(t) y(r\_i(t))\big )^\{(n)\}+ v(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t) \] oscillates or tends to zero as $t\rightarrow \infty $, where, $n \ge 1$ is any positive integer, $p_i$, $r_i\in C^\{(n)\}([0,\infty ),\mathbb \{R\})$  and $p_i$ are bounded for each $i=1,2,\dots ,k$. Further, $f\in C([0, \infty ), \mathbb \{R\})$, $g$, $h$, $v$, $u \in C([0, \infty ), [0, \infty ))$, $G$ and $H \in C(\mathbb \{R\},\mathbb \{R\})$. The functional delays $r_i(t)\le t$, $g(t)\le t$ and $h(t)\le t$ and all of them approach $\infty $ as $t\rightarrow \infty $. The results hold when $u\equiv 0$ and $f(t)\equiv 0$. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.},
author = {Rath, R.N., Panda, K.C., Rath, S.K.},
journal = {Archivum Mathematicum},
keywords = {oscillation; non-oscillation; neutral equation; asymptotic behaviour},
language = {eng},
number = {2},
pages = {65-84},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator},
url = {http://eudml.org/doc/298324},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Rath, R.N.
AU - Panda, K.C.
AU - Rath, S.K.
TI - Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 2
SP - 65
EP - 84
AB - In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation \[ \big (y(t)- \sum _{i=1}^k p_i(t) y(r_i(t))\big )^{(n)}+ v(t)G( y(g(t)))-u(t)H(y(h(t))) = f(t) \] oscillates or tends to zero as $t\rightarrow \infty $, where, $n \ge 1$ is any positive integer, $p_i$, $r_i\in C^{(n)}([0,\infty ),\mathbb {R})$  and $p_i$ are bounded for each $i=1,2,\dots ,k$. Further, $f\in C([0, \infty ), \mathbb {R})$, $g$, $h$, $v$, $u \in C([0, \infty ), [0, \infty ))$, $G$ and $H \in C(\mathbb {R},\mathbb {R})$. The functional delays $r_i(t)\le t$, $g(t)\le t$ and $h(t)\le t$ and all of them approach $\infty $ as $t\rightarrow \infty $. The results hold when $u\equiv 0$ and $f(t)\equiv 0$. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.
LA - eng
KW - oscillation; non-oscillation; neutral equation; asymptotic behaviour
UR - http://eudml.org/doc/298324
ER -