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 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.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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