| Title:
|
Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator (English) |
| Author:
|
Rath, R.N. |
| Author:
|
Panda, K.C. |
| Author:
|
Rath, S.K. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
65-84 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
non-oscillation |
| Keyword:
|
neutral equation |
| Keyword:
|
asymptotic behaviour |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 07547202 |
| idMR:
|
MR4448484 |
| DOI:
|
10.5817/AM2022-2-65 |
| . |
| Date available:
|
2022-05-16T10:27:15Z |
| Last updated:
|
2022-08-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150421 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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|
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| . |
