Bounded oscillation of nonlinear neutral differential equations of arbitrary order

Title:

Bounded oscillation of nonlinear neutral differential equations of arbitrary order

Creator:

Yilmaz, Yeter Şahiner and Zafer, Ağacik

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:49e7d6c1-9e58-4c57-a2f4-b5981af0e06e
uuid:49e7d6c1-9e58-4c57-a2f4-b5981af0e06e

Subject:

oscillation, positive solutions, and neutral equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The paper is concerned with oscillation properties of $n$-th order neutral differential equations of the form \[ [x(t)+cx(\tau (t))]^{(n)}+q(t)f\bigl (x(\sigma (t))\bigr )=0,\quad t\ge t_0>0, \] where $c$ is a real number with $|c|\ne 1$, $q\in C([t_0,\infty ),\mathbb R)$, $f\in C(\mathbb R,\mathbb R)$, $\tau ,\sigma \in C([t_0,\infty ),\mathbb R_+)$ with $\tau (t)<t$ and $\lim _{t\rightarrow \infty }\tau (t)=\lim _{t\rightarrow \infty }\sigma (t)=\infty $. Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which $c$ is a function of $t$ and a certain type of a forcing term is present.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

185-195

Source:

Czechoslovak Mathematical Journal | 2001 Volume:51 | Number:1

Harvested from:

CDK

Metadata only:

false