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## Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2003 | 23 | 1 | 39-52
Tytuł artykułu

### Oscillation of delay differential equation with several positive and negative coefficients

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Some sufficient conditions for oscillation of a first order nonautonomuous delay differential equation with several positive and negative coefficients are obtained.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
39-52
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-06-12
poprawiono
2003-06-05
Twórcy
autor
• Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EGYPT
autor
• Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EGYPT
Bibliografia
• [1] H.A. Agwa, On the oscillation of delay differential equations with real coefficients, International Journal of Mathematics and Mathematics Sciences 22 (3) (1999), 573-578.
• [2] O. Arino, I. Gyori and A. Jawhari, Oscillation criteria in delay equation, J. Differential Equ. 53 (1984), 115-123.
• [3] O. Arino, Y.G. Sficas and G. Ladas, On oscillation of some retarded differential equations, Siam J. Math. Anal. 18 (1987), 64-73.
• [4] Y. Cheng, Oscillation in nonautonomous scalar differential equations with deviating arguments, Proc. AMS 110 (1990), 711-719.
• [5] E.M. Elabbasy, S.H. Saker and K. Saif, Oscillation of nonlinear delay differential equations with application to models exhibiting the Allee effect, Far East Journal of Mathematical Sciences 1 (4) (1999), 603-620.
• [6] E.M. Elabbasy and S.H. Saker, Oscillation of nonlinear delay differential equations with several positive and negative coefficients, Kyungpook Mathematics Journal 39 (1999), 367-377.
• [7] E.M. Elabbasy, A.S. Hegazi and S.H. Saker, Oscillation to delay differential equations with positive and negative coefficients, Electronic J. Differential Equ. 2000 (13) (2000) 1-13.
• [8] K. Gopalsamy, M.R.S. Kulenovic and G. Ladas, Oscillations and global attractivity in respiratory dynamics, Dynamics and Stability of Systems 4 (2) (1989), 131-139.
• [9] I. Gyori, Oscillation conditions in scalar linear differential equations, Bull. Austral. Math. Soc. 34 (1986), 1-9.
• [10] I. Gyori, Oscillation of retarded differential equations of the neutral and the mixed types, J. Math. Anal. Appl. 141 (1989), 1-20.
• [11] I. Gyori and Ladas, Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford 1991.
• [12] O. Hiroshi, Oscillatory properties of the first order nonlinear functional differential equations, Proceeding of Dynamic Systems and Applications 2 (Atlanta, GA 1995), 443-449.
• [13] C.J. Hua and Y. Joinshe, Oscillation of solutions of a class of first order nonlinear differential equation with time lag, Acta Math. Sci. (Chinese) 15 (4) (1995), 368-375.
• [14] B.R. Hunt and J.A. Yorke, When all solutions of $x'(t) = Σ_{j=1}^m q_i(t) x(t - τ_j(t)) = 0$ oscillate, J. Differential Equ. 53 (1984), 139-145.
• [15] M.R.S. Kulenovic, G. Ladas and A. Meimaridou, On oscillation of nonlinear delay differential equations, Quart. Appl. Math. 45 (1987), 155-164.
• [16] M.R.S. Kulenovic and G. Ladas, Linearized oscillations in population dynamics, Bull. Math. Biol. 44 (1987), 615-627.
• [17] M.R.S. Kulenovic and G. Ladas, Linearized oscillation theory for second order delay differential equations, Canadian Mathematical Society Conference Proceeding 8 (1987), 261-267.
• [18] M.R.S. Kulenovic and G. Ladas, Oscillations of sunflower equation, Quart. Appl. Math. 46 (1988), 23-38.
• [19] M.K. Kwong, Oscillation of first-order delay equations, J. Math. Anal. Appl. 156 (1991), 274-286.
• [20] G. Ladas and I.P. Stavroulakis, Oscillations caused by several retarded and advanced arguments, J. Differential Equ. 44 (1982), 143-152.
• [21] G. Ladas and Y.G. Sciicas, Oscillations of delay differential equations with positive and negative coefficients, Proceedings of the International Conference on Qualitative Theory of Differential Equations, University of Alberta, June 18-20, (1984), 232-240.
• [22] G. Ladas and C. Qian, Linearized oscillations for odd-order neutral delay differential equations, J. Differential Equ. 88 (2) (1990), 238-247.
• [23] G. Ladas and C. Qian, Oscillation and global stability in a delay logistic equation, Dynamics and Stability of Systems 9 (1991), 153-162.
• [24] G. Ladas, C. Qian and J. Yan, A comparison result for oscillation of delay differential equation, Proc. AMS 114 (1992), 939-964.
• [25] Y. Norio, Nonlinear oscillation of first order delay differential equations, Rocky Mountain J. Math. 26 (1) (1996), 361-373.
• [26] C. Qian and G. Ladas, Oscillation in differential equations with positive and negative coefficients, Canad. Math. Bull. 33 (1990), 442-451.
• [27] W. Qirui, Oscillations of first order nonlinear delay differential equations, Ann. Differential Equ. 12 (1) (1996), 99-104.
• [28] L. Rodica, Oscillatory solutions for equations with deviating arguments, Bull. Inst. Politehn. Iasi. Sect. I 36(40) (1-4) (1990), 41-46.
• [29] J.J. Wei, Oscillation of first order sublinear differential equations with deviating arguments, Dongbei Shida Xuebao (1991), no. 3, 5-9 (in Chinese).
• [30] G. Xiping, Y. Jun and C. Sui Sun, Linearized comparison criteria for nonlinear neutral differential equations, Ann. Pollon. Math. 64 (2) (1996), 161-173.
• [31] B.G. Zhang and K. Gopalsamy, Oscillation and non-oscillation in a non-autonomous delay logistic model, Quart. Appl. Math. 46 (1988), 267-273.
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Bibliografia
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