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1

Oscillation of delay differential equations

100%
Džurina J.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
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tom 17
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nr 1-2
97-105
EN
Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.
2
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Oscillation of delay differential equation with several positive and negative coefficients

100%
Elabbasy E., Saker S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2003
|
tom 23
|
nr 1
39-52
EN
Some sufficient conditions for oscillation of a first order nonautonomuous delay differential equation with several positive and negative coefficients are obtained.
3
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Four dimensional matrix characterization of double oscillation via RH-conservative and RH-multiplicative matrices

80%
Patterson R., Lemma M.
Open Mathematics
|
2008
|
tom 6
|
nr 4
581-594
EN
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square RH-conservative) be such that $$ P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {\sigma _{m,n} - \sigma _{\alpha ,\beta } } \right| \leqslant P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {s_{m,n} - s_{\alpha ,\beta } } \right| $$ for each double real bounded sequences {s k;l} where $$ \sigma _{m,n} = \sum\limits_{k,l = 1,1}^{\infty ,\infty } {a_{m,n,k,l,} s_{k,l} } . $$ In addition, other implications and variations are also presented.
4
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Oscillation criteria for second order self-adjoint matrix differential equations

80%
Parhi N., Praharaj P.
Annales Polonici Mathematici
|
1999
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tom 72
|
nr 1
1-14
EN
Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.
5
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Oscillation criteria for a class of nonlinear differential equations of third order

80%
Parhi N., Das P.
Annales Polonici Mathematici
|
1992
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tom 57
|
nr 3
219-229
EN
Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form $y''' + q(t)y' + p(t)y^α = 0$ and y''' + q(t)y' + p(t)f(y) = 0, where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.
6
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Oscillation of third-order delay difference equations with negative damping term

80%
Bohner M., Geetha S., Selvarangam S., Thandapani E.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2018
|
tom 72
|
nr 1
EN
The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.
7
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Oscillation of a forced higher order equation

80%
Kosmala W.
Annales Polonici Mathematici
|
1994-1995
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tom 60
|
nr 2
137-144
EN
We state and prove two oscillation results which deal with bounded solutions of a forced higher order differential equation. One proof involves the use of a nonlinear functional.
8
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Classifications and existence of nonoscillatory solutions of second order nonlinear neutral differential equations

80%
Li W.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 3
283-302
EN
A class of neutral nonlinear differential equations is studied. Various classifications of their eventually positive solutions are given. Necessary and/or sufficient conditions are then derived for the existence of these eventually positive solutions. The derivations are based on two fixed point theorems as well as the method of successive approximations.
9
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New oscillation criteria for first order nonlinear delay differential equations

80%
Tang X., Shen J.
Colloquium Mathematicum
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2000
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tom 83
|
nr 1
21-41
EN
New oscillation criteria are obtained for all solutions of a class of first order nonlinear delay differential equations. Our results extend and improve the results recently obtained by Li and Kuang [7]. Some examples are given to demonstrate the advantage of our results over those in [7].
10
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Oscillatory behaviour of solutions of forced neutral differential equations

80%
Parhi N., Mohanty P.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 1
1-10
EN
Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.
11

Necessary and sufficient conditions for oscillations of delay partial difference equations

80%
Zhang B., Liu S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
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tom 15
|
nr 2
213-219
EN
This paper is concerned with the delay partial difference equation (1) $A_{m+1,n}+A_{m,n+1}-A_{m,n} + Σ_{i=1}^u p_i A_{m-k_i, n-l_i} = 0$ where $p_i$ are real numbers, $k_i$ and $l_i$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.
12
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Oscillations of linear integro-differential equations

70%
Olach R., Šamajová H.
Open Mathematics
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2005
|
tom 3
|
nr 1
98-104
EN
Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are established.
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