Characterization of oscillation of fourth order functional differential equations with deviating arguments

1980 ◽  
Vol 124 (1) ◽  
pp. 345-365 ◽  
Author(s):  
Yuichi Kitamura
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Deviating Arguments ◽  
Functional Differential

scholarly journals Instability in Multi Delay Functional Differential Equations of Fourth Order

2015 ◽  
Vol 55 (1) ◽  
pp. 189-198
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
The Subject ◽  
Functional Differential

AbstractA vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.

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.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals Oscillation Properties for Systems of Higher-Order Partial Differential Equations with Distributed Deviating Arguments

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Youjun Liu ◽  
Jianwen Zhang ◽  
Jurang Yan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Partial Differential ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Functional Differential ◽  
Oscillation Properties

New sufficient conditions are obtained for oscillation for the solutions of systems of a class of higher-order quasilinear partial functional differential equations with distributed deviating arguments. The obtained results are illustrated by example.

Oscillation criteria for fourth-order functional differential equations

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Said Grace ◽  
Martin Bohner ◽  
Ailian Liu
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Functional Differential ◽  
New Criteria

AbstractSome new criteria for the oscillation of all solutions of certain fourth-order functional differential equations are established.

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