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1
Content available remote Oscillation theorems for third order neutral delay difference equation with negative coefficient in the neutral term
Jesinthaangel R., Gomathi Jawahar G.
Przegląd Elektrotechniczny
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2022
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R. 98, nr 3
36--38
EN
The article describes the new oscillation criteria which improves the existing results for the third order neutral delay difference equation with the negative coefficient in the neutral term is obtained. Where are positive sequences.
PL
W artykule opisano nowe kryteria oscylacji, które poprawiają dotychczasowe wyniki dla równania różnicy opóźnienia neutralnego trzeciego rzędu z ujemnym współczynnikiem w członie neutralnym. Gdzie są sekwencje dodatnie.
2
Content available Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation
Graef J. R., Tunc E., Grace S. R.
Opuscula Mathematica
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2017
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Vol. 37, no. 6
839--852
EN
This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.
3
Content available Oscillation criteria for third order nonlinear delay differential equations with damping
Grace S. R.
Opuscula Mathematica
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2015
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Vol. 35, no. 4
485--497
EN
This note is concerned with the oscillation of third order nonlinear delay differential equations of the form (r2(t) (r1(t)y'(t))')' +p(t)y'(t) + q(t)ƒ(y(g(t))) = 0. (*) In the papers [A.Tiryaki, M.F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M.F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear-functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation (*) oscillates or converges to zero, provided that the second order equation (r2(t)z'(t))' + (p(t)/r1(t))z(t) =0 (**) is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (*) oscillates if equation (**) is nonoscillatory. We also establish results for the oscillation of equation (*) when equation (**) is oscillatory.
4
An oscillation criteria for third order neutral delay differential equations
Han Z., Li T., Sun S., Zhang C.
Journal of Applied Analysis
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2010
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Vol. 16, nr 2
295-303
EN
In this paper, we will establish some oscillation criteria for the third-order neutral delay differential equations (x(t) - a(t)x(τ (t)))''' + p(t)x(δ (t)) = 0, t ≥ t 0. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations. Our results in this paper extend the results given in [Hanan, Oscillation criteria for third order differential equations, Pacific J. Math. 11 (1961) 919-944]. Some examples are considered to illustrate the main results.
5
Content available Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
Schmeidel E.
Opuscula Mathematica
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2006
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Vol. 26, no. 2
361-369
EN
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
6
Content available Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
Mikołajski J., Schmeidel E.
Opuscula Mathematica
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2006
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Vol. 26, no. 2
343-349
EN
Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
7
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.
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