scholarly journals Oscillation criteria for half-linear function differential equations with damping

2014 ◽  
Vol 18 (5) ◽  
pp. 1537-1542 ◽  
Author(s):  
Jun Liu ◽  
Hong-Ying Luo ◽  
Xi Liu
Keyword(s):  
Differential Equations ◽  
Linear Function ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Functional Differential ◽  
Integral Average

In this paper, a class of half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and integral average skills, new oscillation criteria are obtained which generalize and improve some known results.

scholarly journals Oscillatory Criteria for Higher Order Functional Differential Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peiguang Wang ◽  
Hai Cai
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

We investigate a class of higher order functional differential equations with damping. By using a generalized Riccati transformation and integral averaging technique, some oscillation criteria for the differential equations are established.

scholarly journals New Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Quanxin Zhang ◽  
Li Gao ◽  
Shouhua Liu ◽  
Yuanhong Yu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper discusses oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, three new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve the earlier ones.

scholarly journals The Oscillatory of Linear Conformable Fractional Differential Equations of Kamenev Type

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Hui Liu ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Average Method ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Fractional Differential ◽  
Integral Average

In this paper, the oscillatory of the Kamenev-type linear conformable fractional differential equations in the form of ptyα+1tα+yα+1t+qtyt=0 is studied, where t≥t0 and 0<α≤1. By employing a generalized Riccati transformation technique and integral average method, we obtain some oscillation criteria for the equation. We also give some examples to illustrate the significance of our results.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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