On a class of first order nonlinear functional differential equations of neutral type
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Jaroslav Jaroš, Takaŝi Kusano (1990)
Czechoslovak Mathematical Journal
Papaschinopoulos, Garyfalos (1994)
International Journal of Mathematics and Mathematical Sciences
Györi, Istvan (1991)
International Journal of Mathematics and Mathematical Sciences
Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)
Kybernetika
This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...
Qing-Long Han (2001)
International Journal of Applied Mathematics and Computer Science
This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.
Leszek Olszowy (2010)
Collectanea Mathematica
N. Parhi, Sunita Chand (2000)
Mathematica Slovaca
Rath, Radhanath, Mishra, Prayag Prasad, Padhy, Laxmi Narayan (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Eva Špániková (2004)
Archivum Mathematicum
We study oscillatory properties of solutions of the systems of differential equations of neutral type.
N. Parhi, R. N. Rath (2003)
Annales Polonici Mathematici
Sufficient conditions are obtained so that every solution of where n ≥ 2, p,f ∈ C([0,∞),ℝ), Q ∈ C([0,∞),[0,∞)), G ∈ C(ℝ,ℝ), τ > 0 and σ ≥ 0, oscillates or tends to zero as . Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that . Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞.
N. Parhi, Radhanath N. Rath (2003)
Czechoslovak Mathematical Journal
In this paper, necessary and sufficient conditions are obtained for every bounded solution of to oscillate or tend to zero as for different ranges of . It is shown, under some stronger conditions, that every solution of oscillates or tends to zero as . Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.
N. Parhi, Arun Kumar Tripathy (2005)
Mathematica Slovaca
N. Parhi, Arun Kumar Tripathy (2004)
Mathematica Slovaca
Philos, Christos G., Purnaras, Ioannis K. (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Silviu-Iulian Niculescu (2001)
Kybernetika
This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.
Mikhail Kamenskii, Valeri Obukhovskii, Jen-Chih Yao (2013)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.
John R. Graef, Djamila Beldjerd, Moussadek Remili (2022)
Mathematica Bohemica
The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.
Leonid Berezansky, Elena Braverman (2019)
Czechoslovak Mathematical Journal
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays where and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
Blanka Baculíková, Jozef Džurina (2010)
Open Mathematics
The objective of this paper is to study asymptotic properties of the third-order neutral differential equation . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.
Christos G. Philos, Ioannis K. Purnaras (2007)
Archivum Mathematicum
Autonomous linear neutral delay and, especially, (non-neutral) delay difference equations with continuous variable are considered, and some new results on the behavior of the solutions are established. The results are obtained by the use of appropriate positive roots of the corresponding characteristic equation.
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