Existence of positive solutions for a class of higher order neutral functional differential equations
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 573-583
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
The higher order neutral functional differential equation \[ \frac{\mathrm{d}^n}{\mathrm{d}t^n} \bigl [x(t) + h(t) x(\tau (t))\bigr ] + \sigma f\bigl (t,x(g(t))\bigr ) = 0 \qquad \mathrm{(1)}\] is considered under the following conditions: $n\ge 2$, $\sigma =\pm 1$, $\tau (t)$ is strictly increasing in $t\in [t_0,\infty )$, $\tau (t)$ for $t\ge t_0$, $\lim _{t\rightarrow \infty } \tau (t)= \infty $, $\lim _{t\rightarrow \infty } g(t) = \infty $, and $f(t,u)$ is nonnegative on $[t_0,\infty )\times (0,\infty )$ and nondecreasing in $u \in (0,\infty )$. A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).
The higher order neutral functional differential equation \[ \frac{\mathrm{d}^n}{\mathrm{d}t^n} \bigl [x(t) + h(t) x(\tau (t))\bigr ] + \sigma f\bigl (t,x(g(t))\bigr ) = 0 \qquad \mathrm{(1)}\] is considered under the following conditions: $n\ge 2$, $\sigma =\pm 1$, $\tau (t)$ is strictly increasing in $t\in [t_0,\infty )$, $\tau (t)$ for $t\ge t_0$, $\lim _{t\rightarrow \infty } \tau (t)= \infty $, $\lim _{t\rightarrow \infty } g(t) = \infty $, and $f(t,u)$ is nonnegative on $[t_0,\infty )\times (0,\infty )$ and nondecreasing in $u \in (0,\infty )$. A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).
@article{CMJ_2001_51_3_a9,
author = {Tanaka, Satoshi},
title = {Existence of positive solutions for a class of higher order neutral functional differential equations},
journal = {Czechoslovak Mathematical Journal},
pages = {573--583},
year = {2001},
volume = {51},
number = {3},
mrnumber = {1851548},
zbl = {1079.34538},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a9/}
}
TY - JOUR AU - Tanaka, Satoshi TI - Existence of positive solutions for a class of higher order neutral functional differential equations JO - Czechoslovak Mathematical Journal PY - 2001 SP - 573 EP - 583 VL - 51 IS - 3 UR - http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a9/ LA - en ID - CMJ_2001_51_3_a9 ER -
Tanaka, Satoshi. Existence of positive solutions for a class of higher order neutral functional differential equations. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 573-583. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a9/