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Sufficient oscillation conditions involving $lim sup$ and $lim inf$ for first-order differential equations with non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples, numerically solved in MATLAB, are also given to illustrate the applicability and strength of the obtained conditions over known ones.

Oscillation in linear differential equations

Neuman, František (1973)

Proceedings of Equadiff III

Oscillation in neutral equations with an “integrally small” coefficient.

Yu, J.S., Chen, Ming-Po (1994)

International Journal of Mathematics and Mathematical Sciences

Oscillation in neutral partial functional-differential equations and inequalities.

Fu, Xilin, Wu, Jianhong (1998)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillation in second order functional equations with deviating arguments.

Singh, Bhagat (1981)

International Journal of Mathematics and Mathematical Sciences

Oscillation in second order linear delay differential equations with nonlinear impulses

Zhi Min He, Weigao Ge (2002)

Mathematica Slovaca

Oscillation of a class of higher order neutral differential equations

Pei Guang Wang, Min Wang (2004)

Archivum Mathematicum

In this paper, we investigate a class of higher order neutral functional differential equations, and obtain some new oscillatory criteria of solutions.

Oscillation of a forced higher order equation

Witold A. J. Kosmala (1994)

Annales Polonici Mathematici

We state and prove two oscillation results which deal with bounded solutions of a forced higher order differential equation. One proof involves the use of a nonlinear functional.

Oscillation of a forced nonlinear differential equation

Magdalena Vencková (1984)

Archivum Mathematicum

Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients

Julio G. Dix, Dillip Kumar Ghose, Radhanath Rath (2009)

Mathematica Bohemica

We obtain sufficient conditions for every solution of the differential equation ${[y (t) - p (t) y (r (t))]}^{(n)} + v (t) G (y (g (t))) - u (t) H (y (h (t))) = f (t)$ to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation ${[y (t) - p (t) y (r (t))]}^{(n)} + q (t) G (y (g (t))) = f (t)$ when $q (t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.

Oscillation of a second order delay differential equations

Jozef Džurina (1997)

Archivum Mathematicum

In this paper, we study the oscillatory behavior of the solutions of the delay differential equation of the form ${(\frac{1}{r (t)} y^{'} (t))}^{'} + p (t) y (τ (t)) = 0 .$ The obtained results are applied to n-th order delay differential equation with quasi-derivatives of the form $L_{n} u (t) + p (t) u (τ (t)) = 0 .$

Oscillation of Bôcher's pairs with respect to halflinear second order diff. equ.-s

Bihari, Imre (1982)

Equadiff 5

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