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## Open Mathematics

2012 | 10 | 2 | 807-823
Tytuł artykułu

### Oscillations of difference equations with general advanced argument

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $$\nabla x(n) - p(n)x(\tau (n)) = 0, n \geqslant 1,$$ where {p(n)} is a sequence of nonnegative real numbers, {τ(n)} is a sequence of positive integers such that $$\tau (n) \geqslant n + 1, n \geqslant 1,$$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
807-823
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-01-18
Twórcy
autor
• School of Pedagogical and Technological Education (ASPETE)
autor
• University of Ioannina
Bibliografia
• [1] Berezansky L., Braverman E., Pinelas S., On nonoscillation of mixed advanced-delay differential equations with positive and negative coefficients, Comput. Math. Appl., 2009, 58(4), 766–775 http://dx.doi.org/10.1016/j.camwa.2009.04.010
• [2] Chatzarakis G.E., Koplatadze R., Stavroulakis I.P., Optimal oscillation criteria for first order difference equations with delay argument, Pacific J. Math., 2008, 235(1), 15–33 http://dx.doi.org/10.2140/pjm.2008.235.15
• [3] Chatzarakis G.E., Koplatadze R., Stavroulakis I.P., Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal., 2008, 68(4), 994–1005 http://dx.doi.org/10.1016/j.na.2006.11.055
• [4] Dannan F.M., Elaydi S.N., Asymptotic stability of linear difference equations of advanced type, J. Comput. Anal. Appl., 2004, 6(2), 173–187
• [5] El’sgol’ts L.E., Introduction to the Theory of Differential Equations with Deviating Arguments, Holden-Day, San Francisco, 1966
• [6] Fukagai N., Kusano T., Oscillation theory of first order functional-differential equations with deviating arguments, Ann. Mat. Pura Appl., 1984, 136(1), 95–117 http://dx.doi.org/10.1007/BF01773379
• [7] Győri I., Ladas G., Oscillation Theory of Delay Differential Equations, Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York, 1991
• [8] Koplatadze R.G., Chanturija T.A., Oscillating and monotone solutions of first-order differential equations with deviating argument, Differ. Uravn., 1982, 18(2), 1463–1465 (in Russian)
• [9] Kulenovic M.R., Grammatikopoulos M.K., Some comparison and oscillation results for first-order differential equations and inequalities with a deviating argument, J. Math. Anal. Appl., 1988, 131(1), 67–84 http://dx.doi.org/10.1016/0022-247X(88)90190-4
• [10] Kusano T., On even-order functional-differential equations with advanced and retarded arguments, J. Differential Equations, 1982, 45(1), 75–84 http://dx.doi.org/10.1016/0022-0396(82)90055-9
• [11] Ladas G., Stavroulakis I.P., Oscillations caused by several retarded and advanced arguments, J. Differential Equations, 1982, 44(1), 134–152 http://dx.doi.org/10.1016/0022-0396(82)90029-8
• [12] Li X., Zhu D., Oscillation and nonoscillation of advanced differential equations with variable coefficients, J. Math. Anal. Appl., 2002, 269(2), 462–488 http://dx.doi.org/10.1016/S0022-247X(02)00029-X
• [13] Li X., Zhu D., Oscillation of advanced difference equations with variable coefficients, Ann. Differential Equations, 2002, 18(2), 254–263
• [14] Onose H., Oscillatory properties of the first-order differential inequalities with deviating argument, Funkcial. Ekvac., 1983, 26(2), 189–195
• [15] Zhang B.G., Oscillation of the solutions of the first-order advanced type differential equations, Sci. Exploration, 1982, 2(3), 79–82
Typ dokumentu
Bibliografia
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