scholarly journals Integral averaging technique for oscillation of damped half-linear oscillators

2018 ◽  
Vol 68 (3) ◽  
pp. 755-770 ◽  
Author(s):  
Yukihide Enaka ◽  
Masakazu Onitsuka
Keyword(s):  
Averaging Technique ◽  
Integral Averaging Technique

scholarly journals Multiple Techniques for Studying Asymptotic Properties of a Class of Differential Equations with Variable Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1112
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Method ◽  
Variable Coefficients ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
Oscillatory Properties

This manuscript is concerned with the oscillatory properties of 4th-order differential equations with variable coefficients. The main aim of this paper is the combination of the following three techniques used: the comparison method, Riccati technique and integral averaging technique. Two examples are given for applying the criteria.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

scholarly journals Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 86
Author(s):  
Yang-Cong Qiu ◽  
Kuo-Shou Chiu ◽  
Said R. Grace ◽  
Qingmin Liu ◽  
Irena Jadlovská
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Neutral Dynamic Equations ◽  
Oscillation Of Solutions

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals Some Oscillation Results for Linear Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Nan Wang ◽  
Fanwei Meng
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Linear Hamiltonian Systems ◽  
Interval Oscillation ◽  
Generalized Matrix ◽  
Positive Functionals

The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian systemU′=A(t)U+B(t)V,V′=C(t)U−A∗(t)V. By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.

scholarly journals An Improved Criterion for the Oscillation of Fourth-Order Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 610 ◽  
Author(s):  
Omar Bazighifan ◽  
Marianna Ruggieri ◽  
Andrea Scapellato
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Variable Coefficients ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
Oscillation Of Solutions

The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients r ν w ‴ ν β ′ + ∑ i = 1 j q i ν y κ g i ν = 0 , where ν ≥ ν 0 and w ν : = y ν + p ν y σ ν . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria.

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