Results 261 to 270 of about 76,854 (299)

Neutral Differential Equations

2012
Chapter 6 deals with nonoscillation and oscillation properties of scalar linear neutral differential equations. There are two kinds of neutral equations, one of them can be integrated leading to a term with a concentrated delay and an integral term; the second type which is considered in this chapter has a derivative involved both without a delay and ...
Ravi P. Agarwal, Leonid Berezansky, Elena Braverman, Alexander Domoshnitsky   +3 more
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Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations

Zeitschrift für Analysis und ihre Anwendungen, 1997
In this paper; we establish the equivalence of the oscillation of the two equations (x(t) - x(t - r))^{(n)} + p(t) x(t - \sigma) = 0 \ \ \ \mathrm {and} \ \ \ x^{(n+1)}(t) + \frac{p(t)}{r} x(t) = 0 where
Zhang, B. G., Yang, Bo
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On Some Conjectures on Neutral Differential Equations

Canadian Mathematical Bulletin, 1991
AbstractIn [2], Ladas and Sficas made two conjectures about the asymptotic behavior of solutions of some neutral differential equations. In this paper we confirm that these conjectures are indeed correct.
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Oscillation of Neutral Functional Differential Equations

Acta Mathematica Hungarica, 2000
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Neutral Mixed Type Functional Differential Equations

Journal of Dynamics and Differential Equations, 2015
The authors consider implicitly defined equations of mixed type which arose from examining electrical signaling in cardiac tissue and nerve conduction models. They are studying travelling wave solutions \((\phi,c)\) with \(\phi\) waveform and wave speed \(c\) which satisfy the following equation: \[ \sum\limits^N_{j=1}B_j(\xi)\left[-c\phi'(\xi+r_j)+f ...
Lamb, Charles, Van Vleck, Erik S.
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On solutions of a neutral differential equation with deviating argument

Mathematical and Computer Modelling, 2006
We prove a theorem on the existence and asymptotic behaviour of solutions of a differential equation with a deviating argument of neutral type. The considered equation contains both delayed and advanced arguments. The method used in the proof of our main
Cabrera, I. J., Banaś, J.
exaly   +2 more sources

PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia, 2001
The problem of periodic solutions for nonlinear neutral functional-differential equations \[ \frac{d}{dt}D(t, x_t)=f(t,x_t) \] is discussed by using coincidence degree theory. A new result on the existence of periodic solutions is obtained.
Peng, Shiguo, Zhu, Siming
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OSCILLATIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia, 1992
This paper presents sufficient conditions for all the solutions of some classes of neutral functional differential equations (NFDE) to oscillate. Under consideration are (i) a class of NFDE of retarded type \[ [x(t)- px(t-\tau)]'+\sum^ n_{i=1}q_ ix(t-\sigma_ i)=0, \tag{1} \] where \(p\geq 0\), \(\tau\), \(q_ i\) and the \(\sigma_ i\) are positive ...
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Oscillatory Phenomena in Neutral Delay Differential Equations

Acta Mathematica Hungarica, 1997
Consider the general odd-order delay differential equation of the type \[ x^{(n)}(t)+\sum^m_{i=1} q_ix(t-\sigma_i)=0. \tag{*} \] The authors show that if \(n\) is odd and \[ \frac 1n \left(\sum^m_{i=1}\sigma^n_i q_i\right)^{1/n}>\frac 1e \] then every solution to (*) oscillates.
Das, P., Mishra, B. B.
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Relative Controllability of Neutral Differential Equations with a Delay

SIAM Journal on Control and Optimization, 2017
The authors investigate the relative controllability of the delay-differential system of neutral type \[ \dot{x}(t) - C\dot{x}(t-\tau) = B x(t-\tau) + b u(t) \] when the matrices \(B\) and \(C\) commute. The fundamental solution of this system is piecewise polynomial; its expression, derived in [\textit{M. Pospíšil} and \textit{L.
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