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On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients

In: Mathematica Slovaca, vol. 64, no. 2
John R. Graef - S. Panigrahi - P. Rami Reddy

Details:

Year, pages: 2014, 347 - 366
Keywords:
oscillation, neutral dynamic equations, existence of positive solutions, asymptotic behavior, time scales
About article:
In this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form \begin{equation*} (r(t)(y(t)+p(t)y(α1(t)))^{{Δ}2})^{{Δ}2} + q(t)G(y(α2(t)))-h(t)H(y(α3(t)))=0 \tag{H} \end{equation*} and \begin{equation*} (r(t)(y(t)+p(t)y(α1(t)))^{{Δ}2})^{{Δ}2} +q(t)G(y(α2(t)))-h(t)H(y(α3(t)))=f(t), \tag{NH} \end{equation*} are studied on a time scale \mathbb{T}$ under the assumption that $\intt0 ((t) / (r(t)))Δ t=∞$ and for various ranges of $p(t)$. In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel'skii's fixed point theorem.
How to cite:
ISO 690:
Graef, J., Panigrahi, S., Reddy, P. 2014. On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients. In Mathematica Slovaca, vol. 64, no.2, pp. 347-366. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0209-7

APA:
Graef, J., Panigrahi, S., Reddy, P. (2014). On oscillatory and asymptotic behavior of fourth order nonlinear neutral delay dynamic equations with positive and negative coefficients. Mathematica Slovaca, 64(2), 347-366. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0209-7
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