Oscillation of first order neutral differential equations with positive and negative coefficients

• Autores: Jurang Yan, Wantong Li
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 50, Fasc. 2, 1999, págs. 199-210
• Idioma: inglés
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• Resumen

  • We obtain some new sharp sufficient conditions for the oscillation of all solutions of the first order neutral differential equation with positive and negative coefficients of the form $$\frac{d}{dt}\bigl(x(t) - R(t)x(t - r)\bigr)+ P(t)x(t - \tau ) - Q(t)x(t -\delta) = 0$$ where $P,Q,R\in C([t_0,\infty),R^^), r\in (0,\infty)$ and $\tau,\delta\in R^+$. In particular, the conditions are necessary and sufficient when the coefficients are constants. As corollaries, many known results are extended and improved in the literature.

• Referencias bibliográficas
  • O. Arino and I. Gyori, Necessary and sufficient conditions for oscillation of a neutral differential system with several delays, J. Differential...
  • Q. Chuanxi and G. Ladas, Oscillation of neutral differential equations with variable coefficients, Appl. Anal. 32 (1989), 215–228.
  • Q. Chanxi, G. Ladas, B.G. Zhang and T. Zhao, Sufficient conditions for oscillation and existence of positive solutions, Appl. Anal. 35 (1990),...
  • Q. Chuanxi and G. Ladas, Oscillation in differential equations with positive and negative coefficients, Canad. Math. Bull. 33 (1990), 442–451.
  • K. Farrell, E.A. Grove and G. Ladas, Neutral delay differential equations with positive and negative coefficients, Appl. Anal. 27 (1988),...
  • I. Gyori, On the oscillatory behavior of solutions of certain nonlinear and linear delay differential equations, Nonlinear Analysis TMA 8...
  • I. Gyori and G. Ladas, Oscillatory Theory of Delay Differential Equations with Applications, Oxford Univ. Press (Clarendon), London, New York,...
  • G. Ladas and Y.G. Sficas, Oscillation of higher order neutral equations, J. Austral. Math. Soc. Ser. b 27 (1986), 502–511.
  • B.S. Lalli and B.G. Zhang, Oscillation of first order neutral differential equations, Appl. Anal. 39 (1990), 265–274.
  • W. Li and H.S. Quan, Oscillation of higher order neutral differential equations with positive and negative coefficients, Annals of Differential...
  • X.Z. Qian and L.S. Liao, On the oscillation of the equation $x'(t)+px(t-\tau)-qx(t-\delta)=0$, Annals of Differential Equations...
  • S.G. Ruan, Oscillation for first order neutral differential equations with variable coefficients, Bull. Austral. Math. Soc. 43 (1991), 147–152.
  • Z.C. Wang, Necessary and sufficient condition for oscillations, Annals of Differential Equations 5 (1989), 475–487.
  • J.J. Wei, Sufficient and necessary condition for the oscillation of first order differential equations with deviating arguments and applications,...
  • J.S. Yu, Neutral differential equations with positive and negative coefficients, Acta Math. Sinica 34 (1991), 517–523 (in Chinese).
  • J.S. Yu and J. Yan, Oscillation in first order neutral differential equations with integrally small coefficients, J. Math. Anal. Appl. 187...
  • B.G. Zhang, Oscillation of first order neutral functional differential equations, J. Math. Anal. Appl. 139 (1989), 311–318.
  • B.G. Zhang, On the positive solutions of kind of neutral equations, Acta Math. Appl. Sinica 19(2) (1996), 222–230 (in Chinese).