scholarly journals Comparison theorems for the third order trinomial differential equations with delay argument

2009 ◽  
Vol 59 (2) ◽  
pp. 353-370 ◽  
Author(s):  
Jozef Džurina ◽  
Renáta Kotorová
Keyword(s):  
Differential Equations ◽  
Comparison Theorems ◽  
Third Order ◽  
Delay Argument ◽  
The Third ◽  
Equations With Delay

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 Oscillation theorems for third order neutral differential equations

2012 ◽  
Vol 28 (2) ◽  
pp. 199-206
Author(s):  
BLANKA BACULIKOVA ◽  
◽  
J. DZURINA ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Order Equation ◽  
Comparison Theorems ◽  
Third Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
The Third ◽  
Oscillation Theorems

The aim of this paper is to study the asymptotic properties and the oscillation of the third order neutral differential equations ... Obtained results are based on the new comparison theorems, that permit to reduce the problem of the oscillation of the third order equation to the oscillation of the couple of the first order equation. Obtained comparison principles essentially simplify the examination of the studied equations.

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 Comparison theorems of Hille-Wintner type for third order linear differential equations

1980 ◽  
Vol 21 (2) ◽  
pp. 175-188 ◽  
Author(s):  
L. Erbe
Keyword(s):  
Differential Equations ◽  
Linear Equation ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Linear Differential

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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