scholarly journals Oscillation Criteria for Delay and Advanced Differential Equations with Nonmonotone Arguments

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
George E. Chatzarakis ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Nonnegative Coefficients

We study the oscillatory behavior of differential equations with nonmonotone deviating arguments and nonnegative coefficients. New oscillation criteria, involving lim sup and lim inf, are obtained based on an iterative method. Examples, numerically solved in MATLAB, are given to illustrate the applicability and strength of the obtained conditions over known ones.

scholarly journals Oscillatory behavior of nonlinear differential equations with deviating arguments

1985 ◽  
Vol 31 (1) ◽  
pp. 127-136 ◽  
Author(s):  
S.R. Grace ◽  
B.S. Lalli
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Image Position

New oscillation criteria for nonlinear differential equations with deviating arguments of the formn even, are established.

scholarly journals Oscillation in deviating differential equations using an iterative method

2019 ◽  
Vol 27 (2) ◽  
pp. 143-169 ◽  
Author(s):  
George E. Chatzarakis ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Gronwall Inequality ◽  
Deviating Arguments ◽  
First Order ◽  
Grönwall Inequality ◽  
Nonnegative Coefficients ◽  
First Order Differential Equations

AbstractSufficient 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.

scholarly journals Oscillations in difference equations with several arguments using an iterative method

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 255-273 ◽  
Author(s):  
George Chatzarakis ◽  
Irena Jadlovska
Keyword(s):  
Iterative Method ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Nonnegative Coefficients

This paper presents new sufficient conditions, involving lim sup, for the oscillation of all solutions of difference equations with non-monotone deviating arguments and nonnegative coefficients. We establish these criteria by applying an iterative method. We consider difference equations of both the retarded and the advanced type. We illustrate the results and the improvement over other known oscillation criteria by examples, numerically solved in MATLAB.

scholarly journals Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 412 ◽  
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Type Criterion ◽  
Even Order

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using the technique of Riccati transformation and comparison principles with the second-order differential equations, we obtain a new Philos-type criterion. Our results extend and improve some known results in the literature. An example is given to illustrate our main results.

scholarly journals Oscillation theorems for second order nonlinear differential equations with deviating arguments

1987 ◽  
Vol 10 (1) ◽  
pp. 35-45 ◽  
Author(s):  
S. R. Grace ◽  
B. S. Lalli
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillatory Behaviour ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Oscillation Theorems

New oscillation criteria for the oscillatory behaviour of the differential(a(t)x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0                ,( · =ddt)and(a(t)ψ(x(t))x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0,are established

Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms

2019 ◽  
Vol 69 (5) ◽  
pp. 1117-1126
Author(s):  
Said R. Grace ◽  
John R. Graef ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Linear Delay ◽  
Delay Differential

Abstract This article concerns the oscillatory behavior of solutions to second-order half-linear delay differential equations with mixed neutral terms. The authors present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated with examples.

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