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Oscillation of solutions to non-linear difference equations with several advanced arguments

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Języki publikacji
EN
Abstrakty
EN
This work concerns the oscillation and asymptotic properties of solutions to the non-linear difference equation with advanced arguments [formula]. We establish sufficient conditions for the existence of positive, and negative solutions. Then we obtain conditions for solutions to be bounded, convergent to positive infinity and to negative infinity and to zero. Also we obtain conditions for all solutions to be oscillatory.
Rocznik
Strony
887--898
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • RUDN University 6 Miklukho-Maklay St. Moscow, 117198, Russia
autor
  • Department of Mathematics Texas State University 601 University Drive San Marcos, TX 78666, USA
Bibliografia
  • [1] R. Agarwal, L. Berezansky, E. Braverman, A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer, New York, Dordrecht, Heidelberg, London, 2012.
  • [2] L. Berezansky, E. Braverman, S. Pinelas, On nonosdilation of mixed advanced-delay differential equations with positive and negative coefficients, Comput. Math. Appl. 58 (2009) 4, 766-775.
  • [3] F.M. Dannan, S.N. Elaydi, Asymptotic stability of linear difference equations of advanced type, J. Comput. Anal. Appl. 6 (2004) 2, 173-187.
  • [4] L.E. EFsgoFc, Introduction to the Theory of Differential Equations with Deviating Arguments, Holden-Day, Inc., San Francisco, 1966.
  • [5] L.H. Erbe, B.G. Zhang, Odllation of discrete analogues of delay equations, Differential and Integral Equations 2 (1989) 3, 300-309.
  • [6] N. Fukagai, T. Kusano, Oscillation theory of first order functional-differential equations with deviating arguments, Ann. Mat. Pura Appl. 136 (1984) 1, 95-117.
  • [7] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York, 1991.
  • [8] R.G. Koplatadze, T.A. Chanturija, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differ. Uravn. 18 (1982) 2, 1463-1465 [in Russian].
  • [9] M.R. Kulenovic, M.K. Grammatikopoulos, Some comparison and oscillation results for first-order differential equations and inequalities with a deviating argument, J. Math. Anal. Appl. 131 (1988) 1, 67-84.
  • [10] T. Kusano, On even-order functional-differential equations with advanced and retarded arguments, J. Differential Equations 45 (1982) 1, 75-84.
  • [11] G. Ladas, I.P. Stavroulakis, Oscillations caused by several retarded and advanced arguments, J. Differential Equations 44 (1982) 1, 134-152.
  • [12] X. Li, D. Zhu, Oscillation and nonosdilation of advanced differential equations with variable coefficients, J. Math. Anal. Appl. 269 (2002) 2, 462-488.
  • [13] X. Li, D. Zhu, Oscillation of advanced difference equations with variable coefficients, Ann. Differential Equations 18 (2002) 2, 254-263.
  • [14] H. Onose, Oscillatory properties of the first-order differential inequalities with deviating argument, Funkcial. Ekvac. 26 (1983) 2, 189-195.
  • [15] S. Pinelas, Asymptotic behavior of solutions to mixed type differential equations, Electron. J. Differential Equations 2014 (2014) 210, 1-9.
  • [16] S. Stevic, On some solvable difference equations and systems of difference equations, Abstr. Appl. Anal. 2012 (2012), 11 pp.
  • [17] S. Stevic, On a solvable system of difference equations of kth order, Appl. Math. Comput. 219 (2013), 7765-7771.
  • [18] S. Stevic, M.A. Alghamdi, A. Alotaibi, N. Shahzad, On a higher-order system of difference equations, Electron. J. Qual. Theory Differ. Equ. Art. (2013), Article ID 47, 1-18.
  • [19] B.G. Zhang, Oscillation of the solutions of the first-order advanced type differential equations, Sci. Exploration 2 (1982) 3, 79-82.
Uwagi
PL
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5a74a43b-7f8e-4ed0-ac00-409b785ed83e
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