Forced oscillations of first order nonlinear neutral differential equations.
Tanaka, S. (1997)
Journal of Applied Analysis
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Tanaka, S. (1997)
Journal of Applied Analysis
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Ireneusz Kubiaczyk, Samir H. Saker (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear case. Some examples are considered to illustrate our main results.
Wantong Li (1997)
Annales Polonici Mathematici
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A class of neutral nonlinear differential equations is studied. Various classifications of their eventually positive solutions are given. Necessary and/or sufficient conditions are then derived for the existence of these eventually positive solutions. The derivations are based on two fixed point theorems as well as the method of successive approximations.
Elabbasy, E. M., Hassan, T. S. (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 34K15, 34C10. In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation (x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0, where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.
Wan-Tong Li, S. H. Saker (2001)
Annales Polonici Mathematici
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We consider nonlinear neutral delay differential equations with variable coefficients. Finite and infinite integral conditions for oscillation are obtained. As an example, the neutral delay logistic differential equation is discussed.
Hassan, Taher S. (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 34C10, 34C15. It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most...
Tripathy, A.K. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Shao Yuan Huang, Sui Sun Cheng (2012)
Annales Polonici Mathematici
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Several recent oscillation criteria are obtained for nonlinear delay impulsive differential equations by relating them to linear delay impulsive differential equations or inequalities, and then comparison and oscillation criteria for the latter are applied. However, not all nonlinear delay impulsive differential equations can be directly related to linear delay impulsive differential equations or inequalities. Moreover, standard oscillation criteria for linear equations cannot be applied...
Gil', M.I. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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N. Parhi, P. K. Mohanty (1996)
Annales Polonici Mathematici
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Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.
Han, Zhenlai, Li, Tongxing, Sun, Shurong, Chen, Weisong (2010)
Advances in Difference Equations [electronic only]
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Li, Tongxing, Han, Zhenlai, Zhao, Ping, Sun, Shurong (2010)
Advances in Difference Equations [electronic only]
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Han, Zhenlai, Li, Tongxing, Zhang, Chenghui, Sun, Ying (2011)
Abstract and Applied Analysis
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