Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients

• Autorzy: Panigrahi S. , Reddy P. R.

Identyfikatory

DOI

10.1515/jaa-2018-0014

• Języki publikacji: EN

Abstrakty

EN

In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. AMath. Anal. 20 (2013), 143-163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 (2013), 11-28]. Examples are included to illustrate the validation of the results.

Słowa kluczowe

EN

oscillation; higher order; nonlinear; neutral dynamic equations; asymptotic behavior; positive and negative coefficients; time scales

PL

drgania; wyższy rząd; nieliniowość; zachowanie asymptotyczne; pozytywne i negatywne współczynniki; skale czasu

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 2
• Strony: 139--154
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Panigrahi S.

• School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India

autor

Reddy P. R.

• School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India

Bibliografia

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• [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
• [3] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
• [4] S. R. Grace, J. R. Graef, S. Panigrahi and E. Tunc, On the oscillatory behavior of even order neutral delay dynamic equations on time scales, Electron. J. Qual. Theory Differ. Equ. 2012 (2012), 1-12.
• [5] S. Hilger, Analysis on measure chains: A unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.
• [6] B. Karpuz, Asymptotic behavior of bounded solutions of a class of higher-order neutral dynamic equations, Appl. Math. Comput. 215 (2009), 2174-2183.
• [7] B. Karpuz, Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients, Electron. J. Qual. Theory Differ. Equ. 2009 (2009), 1-14.
• [8] B. Karpuz, Sufficient conditions for the oscillation and asymptotic behavior of higher-order dynamic equations of neutral type, Appl. Math. Comput. 221 (2013), 453-462.
• [9] B. Karpuz, Volterra theory on time scales, Results Math. 65 (2014), no. 34, 263-292.
• [10] B. Karpuz and Ö. Öcalan, Necessary and sufficient conditions on asymptotic behaviour of solutions of forced neutral delay dynamic equations, Nonlinear Anal. 71 (2009), 3063-3071.
• [11] S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 (2013), 11-28.
• [12] S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 (2013), 143-163.
• [13] P. Rami Reddy and S. Panigrahi, Oscillatory behaviour of higher-order neutral delay dynamic equations with positive and negative coefficients - I (communicated).
• [14] Y. Sahiner Yilmaz and A. Zafer, Bounded oscillation of nonlinear neutral differential equations of arbitrary order, Czechoslovak Math. J. 51 (2001), 185-195.
• [15] Y. Sun, Z. Han, S. Sun and C. Zhang, Oscillation criteria for even order nonlinear neutral differential equations, Electron. J. Qual. Theory Differ. Equ. 2012 (2012), 1-12.
• [16] A. K. Tripathy, Oscillatory behavior of a class of nonlinear second order mixed difference equations, Electron. J. Qual. Theory Differ. Equ. 2010 (2010), 1-19.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).