scholarly journals Asymptotic Properties of Third-Order Nonlinear Differential Equations

2013 ◽  
Vol 54 (1) ◽  
pp. 19-29
Author(s):  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Theorems ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Advanced Case ◽  
The Third ◽  
Functional Differential ◽  
New Criteria

Abstract We present new criteria guaranteeing that all nonoscillatory solutions of the third-order functional differential equation tend to zero. Our results are based on the suitable comparison theorems. We consider both delay and advanced case of studied equation. The results obtained essentially improve and complement earlier ones.

scholarly journals On Properties of Third-Order Differential Equations via Comparison Principles

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
B. Baculíková ◽  
J. Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Canonical Form ◽  
Functional Differential Equation ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Comparison Theorems ◽  
Third Order ◽  
The Third ◽  
Functional Differential

The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation , where studied equation is in a canonical form, that is, . Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

scholarly journals Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
B. Baculíková
Keyword(s):  
Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Comparison Theorems ◽  
Third Order ◽  
Nonlinear Functional ◽  
The Third ◽  
Property B ◽  
Functional Differential ◽  
Mixed Arguments

The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments . Both cases and are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

scholarly journals Asymptotic properties of trinomial delay differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 71-79
Author(s):  
Jozef Džurina ◽  
Renáta Kotorová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Canonical Form ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
The Third ◽  
Delay Differential ◽  
New Criteria

AbstractNew criteria for asymptotic properties of the solutions of the third order delay differential equation, by transforming this equation to its binomial canonical form are presented

scholarly journals Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Miroslav Bartušek ◽  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equation ◽  
Damping Term ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Deviating Argument ◽  
The Third ◽  
Necessary And Sufficient

We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argumentx‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operatorℒx=x‴+q(t)x′is oscillatory.

scholarly journals Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
J. Džurina ◽  
R. Komariková
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Theorems ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third

The aim of this paper is to study properties of the third-order delay trinomial differential equation((1/r(t))y′′(t))′+p(t)y′(t)+q(t)y(σ(t))=0, by transforming this equation onto the second-/third-order binomial differential equation. Using suitable comparison theorems, we establish new results on asymptotic behavior of solutions of the studied equations. Obtained criteria improve and generalize earlier ones.

scholarly journals Dynamics of Third-Order Nonlinear Neutral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Hua Wang ◽  
Li Liu ◽  
Yanxiang Tan
Keyword(s):  
Asymptotic Properties ◽  
Neutral Equation ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Neutral Equations ◽  
The Third ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
New Criteria

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form(r(t)([xt+∫abpt,μxτt,μdμ]′′)α)′+∫cdqt,ξfαxgt,ξdξ=0. Applying suitable generalized Riccati transformation and integral averaging technique, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equation. Obtained results essentially improve and complement earlier ones.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

On solutions of third order nonlinear differential equations

2006 ◽  
Vol 4 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Ivan Mojsej ◽  
Ján Ohriska
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Property A ◽  
Comparison Result ◽  
Third Order ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
The Third

AbstractThe aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

Oscillation criteria for third-order nonlinear differential equations

2008 ◽  
Vol 58 (2) ◽  
Author(s):  
B. Baculíková ◽  
E. Elabbasy ◽  
S. Saker ◽  
J. Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
The Third ◽  
Third Order Differential Equation ◽  
Oscillation Properties

AbstractIn this paper, we are concerned with the oscillation properties of the third order differential equation $$ \left( {b(t) \left( {[a(t)x'(t)'} \right)^\gamma } \right)^\prime + q(t)x^\gamma (t) = 0, \gamma > 0 $$. Some new sufficient conditions which insure that every solution oscillates or converges to zero are established. The obtained results extend the results known in the literature for γ = 1. Some examples are considered to illustrate our main results.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

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