Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 237-253
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Consider the forced higher-order nonlinear neutral functional differential equation \[ \frac{{\mathrm d}^n}{{\mathrm d}t^n}[x(t)+C(t) x(t-\tau )]+\sum ^m_{i=1} Q_i(t)f_i(x(t-\sigma _i))=g(t), \quad t\ge t_0, \] where $n, m \ge 1$ are integers, $\tau , \sigma _i\in {\mathbb{R}}^+ =[0, \infty )$, $C, Q_i, g\in C([t_0, \infty ), {\mathbb{R}})$, $f_i\in C(\mathbb{R}, \mathbb{R})$, $(i=1,2,\dots ,m)$. Some sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general $Q_i(t)$ $(i=1,2,\dots ,m)$ and $g(t)$ which means that we allow oscillatory $Q_i(t)$ $(i=1,2,\dots ,m)$ and $g(t)$. Our results improve essentially some known results in the references.
Consider the forced higher-order nonlinear neutral functional differential equation \[ \frac{{\mathrm d}^n}{{\mathrm d}t^n}[x(t)+C(t) x(t-\tau )]+\sum ^m_{i=1} Q_i(t)f_i(x(t-\sigma _i))=g(t), \quad t\ge t_0, \] where $n, m \ge 1$ are integers, $\tau , \sigma _i\in {\mathbb{R}}^+ =[0, \infty )$, $C, Q_i, g\in C([t_0, \infty ), {\mathbb{R}})$, $f_i\in C(\mathbb{R}, \mathbb{R})$, $(i=1,2,\dots ,m)$. Some sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general $Q_i(t)$ $(i=1,2,\dots ,m)$ and $g(t)$ which means that we allow oscillatory $Q_i(t)$ $(i=1,2,\dots ,m)$ and $g(t)$. Our results improve essentially some known results in the references.
Classification :
34K11, 34K15, 34K40
Keywords: neutral differential equations; nonoscillatory solutions
Keywords: neutral differential equations; nonoscillatory solutions
@article{CMJ_2005_55_1_a17,
author = {Zhou, Yong and Zhang, B. G. and Huang, Y. Q.},
title = {Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations},
journal = {Czechoslovak Mathematical Journal},
pages = {237--253},
year = {2005},
volume = {55},
number = {1},
mrnumber = {2121670},
zbl = {1081.34068},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a17/}
}
TY - JOUR AU - Zhou, Yong AU - Zhang, B. G. AU - Huang, Y. Q. TI - Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations JO - Czechoslovak Mathematical Journal PY - 2005 SP - 237 EP - 253 VL - 55 IS - 1 UR - http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a17/ LA - en ID - CMJ_2005_55_1_a17 ER -
%0 Journal Article %A Zhou, Yong %A Zhang, B. G. %A Huang, Y. Q. %T Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations %J Czechoslovak Mathematical Journal %D 2005 %P 237-253 %V 55 %N 1 %U http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a17/ %G en %F CMJ_2005_55_1_a17
Zhou, Yong; Zhang, B. G.; Huang, Y. Q. Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 237-253. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a17/