PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Oscillation criteria for second-order functional difference equation with neutral terms

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this manuscript, two type of new oscillation criteria are obtained respect to coefficient ak in the following Eq. (1.1). In the subsection 2.1 considered as ak > 0. In the subsection 2.2 allowed it to be an oscillating sequence. There are no results for the oscillation of second order difference equations with oscillating coefficients up to now.
Wydawca
Rocznik
Strony
615--625
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
  • Afyon Kocatepe University Faculty of Science and Literatures Department of Mathematics, Ans Campus 03200 - Afyonkarahisar, Turkey, yasarbolat@aku.edu.tr
Bibliografia
  • [1] Ravi P. Agarwal, Difference Equation and Inequalities, Marcel Dekker. New York, 2000.
  • [2] Ravi P. Agarwal, Advanced Topics in Difference Equations, Kluwer Academic Publishers, London, 1997.
  • [3] Ravi P. Agarwal, S. R. Grace, D. O’Regan, Oscillatory Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, 2000.
  • [4] I. Györi, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon, Ox-ford, 1991.
  • [5] R. E. Mickens, Difference Equations: Theory and Applications, Van Nostrand-Reinhold, New York, 1990.
  • [6] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, 1964.
  • [7] J. J. A. M. Brands, Oscillation theorems for second-order functional differential equations, J. Math. Anal. Appl. 63 (1978) 54-64.
  • [8] A. Cabada, Extremal solutions for the difference φ-Laplacian problem with nonlinear functional boundary conditions, Comput. Math. Appl. 42 (2001) 593-601.
  • [9] S. Chen, L. H. Erbe, Riccati techniques and discrete oscillations, J. Math. Anal. Appl. 142 (1989) 468-487.
  • [10] J. W. Hooker, M. K. Kwong, W. T. Patula, Oscillatory second order linear difference equations, SIAM J. Math. Anal. 18 (1987) 54-63.
  • [11] J. W. Hooker, W. T. Patula, Riccati type transformations for second-order linear difference equations, J. Math. Anal. Appl. 82 (1981) 451-462.
  • [12] J. W. Hooker, W. T. Patula, A second-order nonlinear difference equation: Oscillation and asymptotic behaviour, J. Math. Anal. Appl. 91 (1983) 9-29.
  • [13] H. J. Li, S. S. Cheng, An oscillation theorem for a second order nonlinear difference equation, Utilitas Math. 43 (1993) 155-159.
  • [14] W. T. Li, S. S. Cheng, Oscillation criteria for a nonlinear difference equation, Comput. Math. Appl. 36 (1998) 87-94.
  • [15] W. T. Patula, Growth and oscillation properties of second order linear difference equations, SIAM J. Math. Anal. 10 (1979) 55-61.
  • [16] P. Rehak, Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations, J. Math. Anal. Appl. 252 (2000) 813-827.
  • [17] P. Rehak, Oscillatory criteria for second order half-linear difference equations, J. Differ. Equations Appl. 7 (2001) 483-505.
  • [18] P. Rehak, Generalized discrete Riccati equation and oscillation of halflinear difference equations, Math. Comput. Modelling 34 (2001) 257-269.
  • [19] P. Rehak, Oscillatory properties of second order half-linear difference equations, Czechoslovak Math. J. 51 (2001) 303-321.
  • [20] B. Szmanda, Oscillation of solutions of second order difference equations, Portugal. Math. 37 (1978) 251-54.
  • [21] B. Szmanda, Characterization of oscillation of second order nonlinear difference equations, Bull. Polish Acad. Sci. Math. 34 (1986) 133-141.
  • [22] E. Thandapani, I. Gy ̈ori, B. S. Lalli, An application of discrete inequality to second order nonlinear oscillation, J. Math. Anal. Appl. 186 (1994) 200-208.
  • [23] E. Thandapani, S. Pandian, On the oscillatory behaviour of solutions of second order nonlinear difference equations, Z. Anal. Anwendungen 13 (1994) 347-358.
  • [24] B. G. Zhang, G. D. Chen, Oscillation of certain second order nonlinear difference equations, J. Math. Anal. Appl. 199 (1996) 827-841.
  • [25] Z. Zhang, J. Zhang, Oscillation criteria for second-order functional difference equations with “summation small” coefficient, Comput. Math. Appl. 38 (1999) 25-31.
  • [26] B. G. Zhang, Y. Zhou, Oscillation and nonoscillation for second-order linear difference equations, Comput. Math. Appl. 39 (2000) 1-7.
  • [27] R. P. Agarwal, S. R. Grace, D. O’Regan, On the oscillation of certain second order difference equations, J. Differ. Equations Appl. 9 (2003) 109-119.
  • [28] H. A. El-Morshedy and S. R. Grace, Comparison theorems for second order nonlinear difference equations, J. Math. Anal. Appl. 306 (2005) 106-121.
  • [29] Hong Li, Hou-biao Li and Shou-ming Zhong, Stability of neutral type descriptor system with mixed delays, Chaos, Solitons & Fractals, Volume 33, Issue 5, August 2007, Pages 1796-1800.
  • [30] Ker-Wei Yu and Chang-Hua Lien, Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 20 February 2007,
  • [31] Yongkun Li, Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays, Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 23 October 2006,
  • [32] Ju H. Park and O. M. Kwon, Stability analysis of certain nonlinear differential equation Chaos, Solitons & Fractals, In Press, Corrected Proof, Available online 19 October 2006.
  • [33] Ju H. Park and O. Kwon, Controlling uncertain neutral dynamic systems with delay in control input, Chaos, Solitons & Fractals, Volume 26, Issue 3, November 2005, Pages 805-812.
  • [34] Ju H. Park, Design of dynamic controller for neutral differential systems with delay in control input, Chaos, Solitons & Fractals, Volume 23, Issue 2, January 2005, Pages 503-509.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0049-0013
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.