| Title:
|
Existence of positive solutions for a class of higher order neutral functional differential equations (English) |
| Author:
|
Tanaka, Satoshi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
573-583 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $t\in [t_0,\infty )$, $\tau (t)<t$ 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). (English) |
| Keyword:
|
neutral differential equation |
| Keyword:
|
positive solution |
| MSC:
|
34K11 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1079.34538 |
| idMR:
|
MR1851548 |
| . |
| Date available:
|
2009-09-24T10:45:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127670 |
| . |
| Reference:
|
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