Communications in Mathematical Analysis

Oscillation Results for Fourth-Order Nonlinear Neutral Dynamic Equations

John R. Graef , Saroj Panigrahi , and P. Rami Reddy

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Abstract

In this paper, the authors study the oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form \begin{equation} \tag{H} (r(t)(y(t)+p(t)y(\alpha(t)))^{{\Delta }^2})^{{\Delta }^2} + q(t)G(y(\beta(t)))h(t)H(y(\gamma(t)))=0 \end{equation} and \begin{equation} \tag{NH} (r(t)(y(t)+p(t)y(\alpha(t)))^{{\Delta }^2})^{{\Delta }^2} + q(t)G(y(\beta(t)))h(t)H(y(\gamma(t)))=f(t), \end{equation} where $\mathbb {T}$ is a time scale with $\sup \mathbb {T}=\infty$, $t \in [t_0,\infty)_\mathbb{T}$, and $t_0\geqslant 0$. They assume that $\int _{t_0}^\infty \frac{\sigma (t)}{r(t)}\Delta t \lt \infty$ and obtain results for various ranges of values of $p(t)$. Examples illustrating the results are included.

Article information

Source
Commun. Math. Anal., Volume 15, Number 1 (2013), 11-28.

Dates
First available in Project Euclid: 18 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.cma/1374153492

Mathematical Reviews number (MathSciNet)
MR3082261

Zentralblatt MATH identifier
1280.34094

Subjects
Primary: 34N05, 34C10, 34C15, 34K11

Keywords
Oscillation neutral dynamic equations existence of positive solutions asymptotic behavior time scales

Citation

Panigrahi , Saroj; Graef , John R.; Reddy, P. Rami. Oscillation Results for Fourth-Order Nonlinear Neutral Dynamic Equations. Commun. Math. Anal. 15 (2013), no. 1, 11--28. https://projecteuclid.org/euclid.cma/1374153492


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