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1
Content available Oscillatory behavior of second-order damped differential equations with a superlinear neutral term
Tunc Ercan, Ozdemir Osman
Opuscula Mathematica
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2020
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Vol. 40, no. 5
629--639
EN
. This article concerns the oscillatory behavior of solutions to second-order damped nonlinear differential equations with a superlinear neutral term. The results are obtained by a Riccati type transformation as well as by an integral criterion. Examples illustrating the results are provided and some suggestions for further research are indicated.
2
Content available On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative
Nabil Tamer
Journal of Mathematics and Applications
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2020
|
Vol. 43
99--112
EN
In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.
3
Content available On the exponential stability of a neutral differential equation of first order
Gözen M., Tunç C.
Journal of Mathematics and Applications
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2018
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Vol. 41
95--107
EN
In this work, we establish some assumptions that guaranteeing the global exponential stability (GES) of the zero solution of a neutral differential equation (NDE). We aim to extend and improves some results found in the literature.
4
Content available remote Oscillation properties of a class of nonlinear differential equations of neutral type
Tripathy A. K., Rao K V V S
Fasciculi Mathematici
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2012
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Nr 48
129--144
EN
Oscillatory and asymptotic behaviour of the solutions of a class of nonlinear rst order neutral delay dierential equa- tions with positive and negative coecients of the form E1 ...[wzór] are studied under various ranges of p(t). Sufficient conditions are obtained for the existence of positive bounded solution of (E2).
5
Oscillation criteria for a class of third-order nonlinear neutral differential equations
Zhong J., Ouyang Z., Zou S.
Journal of Applied Analysis
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2011
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Vol. 17, nr 2
155-163
EN
A class of third-order nonlinear neutral differential equation (r(t)(y"(t)) α)' + q(t) f(x(σ (t))) = 0 is investigated in this paper, where y(t) = x(t) + p(t)x(?(t)), and ? > 0 is any quotient of odd integers. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation, and some known oscillation criteria be extended. An example is inserted to illustrate the result.
6
Content available remote Oscillation properties of a class of neutral differential equations with positive and negative coefficients
Tripathy A. K.
Fasciculi Mathematici
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2010
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Nr 45
133-155
EN
In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) ...[wzór] and ...[wzór] are studied under the assumptions ...[wzór] and ...[wzór] for various ranges of p(t). Sufficient conditions are obtained for existence of bounded positive solutions of (E).
7
Content available remote Necessary and sufficient conditions for the solutions of second order neutral differential equations to be oscillatory of tending to zero
Padhi S., Kar P. K., Nayak S. K.
Fasciculi Mathematici
|
2004
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Nr 34
73-83
EN
In this paper, necessary and sufficient conditions have been obtained for a class of forced superlinear second order neutral differential equations of Emden-Fowler type such that every solution of the equation is either oscillatory or tends to zero as t -> niekończoność
8
Content available remote Monotone solutions of a higher-order neutral differential equation
Zhang G., Migda M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2004
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Vol. 44, nr 1
147--162
EN
A continuous function x(t) is said to be (*)-monotone with a positive number τ if x(t) > 0 and (-1)n(x(t) - x(t - τ))(n) ≥ 0 for n ≥ 0. This paper is concerned with various classifications of (*)-monotone solutions of a neutral differential eąuation. Necessary and/or sufficient conditions are then derived for the existence of these solutions.
9
Content available remote Bounded oscillation for a class of even order neutral difference equations
Lin X., Shen J.
Fasciculi Mathematici
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2002
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Nr 33
37-47
EN
We investigate bounded oscillation for the even order neutral delay difference equation delta'' (x(n) -cx(n-m) = pn(x-k), where u is even. The sufficient conditions obtained in this paper improve and generalize the results in related literature.
10
Content available remote Oscillatory properties of third order neutral delay difference equations
Thandapani E., Mahalingam K.
Demonstratio Mathematica
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2002
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Vol. 35, nr 2
325-337
EN
Some new sufficient criteria for the oscillation of all solutions of the neutral difference equation are obtained. Existence of nonoscillatory solution and its asymptotic behavior are also discussed. Examples illustrating the results are inserted.
11
Content available remote Comparison theorems for the oscillation of higher order neutral delay diference equations
Zhou Y., Zhang B. G.
Demonstratio Mathematica
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2002
|
Vol. 35, nr 3
545-555
EN
We obtain a necessary and sufficient condition for the oscillation of the higher order neutral delay difference equation m(Xn -pnxn-r) + f(n, xg1(n),xg2(n), ...,xg1(n))=0 where m > 1 is an odd integer. As some application of this result, we estabilish three comparison theorems for the oscillation of the above equation.
12
Content available remote On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations
Parhi N., Tripathy A. K.
Fasciculi Mathematici
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2001
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Nr 32
83-95
EN
Oscillatory and asymptotic behaviour of solutions of forced first order nonlinear neutral delay difference equations of the from (mathematical formula) is studied under appropriate assumptions on sequences of real numbers {qn} and {q(n) {f(n)} and {fn} and G belong to class C(R, R). The behaviour of solutions of mathematical formula is also discussed where {pa} is allowed to change sign.
13
Content available remote Existence of nonoscillatory solution for linear neutral delay equation
Kulenovic M. R. S., Hadziomerspahic S.
Fasciculi Mathematici
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2001
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Nr 32
61-72
EN
Consider the neutral delay differential equation with positive and negative coefficients (mathematical formula) where p s R and (mathematical formula) We obtain the sufficient condition for the existence of a nonoscillatory solution of the above equation to be (mathematical formula) and certain technical conditions implying thatdominates for large enough, for =-1.
14
Content available remote On the oscillation of odd order neutral differential equations
Zhang B.-G., Li W.
Fasciculi Mathematici
|
1999
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Nr 29
167-183
EN
Consider the odd order neutral differential equation [formula] where [...]l is an oddinteger, [...] Some new sufficient conditions for oscillation of the above equation are obtained. A comparison resu1t is also established.
15
Content available remote A note on unstable neutral differential equations of the second order
Dzurina J., Mihalikova B.
Fasciculi Mathematici
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1999
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Nr 29
17-22
EN
The airn of this paper is to irnprove an existing sufficient conditions for all bounded solutions of the second order neutral differential equation [...] to be oscillatory .
16
Content available remote On the distance between adjacent zerores of solutions of first order neutral differential equations
Zhou Y., Yu Y., Feng B.
Demonstratio Mathematica
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1999
|
Vol. 32, nr 1
31-40
17
Content available remote Comparison theorems for differential equations of neutral type
Ruzickova M., Spanikova E.
Fasciculi Mathematici
|
1998
|
Nr 28
141-148
EN
We are interested in comparing the oscillatory and asymptotic properties of equations [...] with those of the equations [...]
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