Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

Zhou, Yong, Zhang, Bing Gen, and Huang, Y. Q.. "Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations." Czechoslovak Mathematical Journal 55.1 (2005): 237-253. <http://eudml.org/doc/30941>.

@article{Zhou2005,
abstract = {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.},
author = {Zhou, Yong, Zhang, Bing Gen, Huang, Y. Q.},
journal = {Czechoslovak Mathematical Journal},
keywords = {neutral differential equations; nonoscillatory solutions; neutral differential equations; nonoscillatory solutions},
language = {eng},
number = {1},
pages = {237-253},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations},
url = {http://eudml.org/doc/30941},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Zhou, Yong
AU - Zhang, Bing Gen
AU - Huang, Y. Q.
TI - Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 237
EP - 253
AB - 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.
LA - eng
KW - neutral differential equations; nonoscillatory solutions; neutral differential equations; nonoscillatory solutions
UR - http://eudml.org/doc/30941
ER -