Results 171 to 180 of about 45,401 (204)

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
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +1 more source

Oscillation of Neutral Functional Differential Equations

Acta Mathematica Hungarica, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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.
openaire   +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
openaire   +2 more sources

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 ...
openaire   +2 more sources

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.
openaire   +2 more sources

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.
openaire   +1 more source

LOGISTIC DIFFERENTIAL EQUATION OF NEUTRAL TYPE

1997
The following logistic neutral functional-differential equation describes some type of population dynamics (consistent with the experiment on the population of Daphnia magna) accounting retardation due to the processes of growing up and maturation: \[ N'=rN\left(1- {N(t-h)+\rho N'(t-h)\over K}\right) . \] The boundedness and asymptotic stability of its
openaire   +2 more sources