Results 221 to 230 of about 79,942 (257)

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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Neutral fuzzy fractional functional differential equations

Fuzzy Sets and Systems, 2021
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Nguyen Dinh Phu, Vasile Lupulescu, Ngo Van Hoa   +2 more
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Oscillation of Neutral Functional Differential Equations

Acta Mathematica Hungarica, 2000
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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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POSITIVE SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia, 1996
The paper contains sufficient conditions under which the neutral functional differential equation \[ {d\over dx} \left[ x(t)+ \int^t_c x(s)+ d_s \mu(t,s) \right] +\int^t_c f\bigl( t,x(s) \bigr) d_s n(t,s) =0,\;t>t_0\leq c \tag{1} \] has a positive solution on \([c,+\infty)\). The following examples are based on his two theorems. The equation \[ {d\over
Huang, Zhenxun, Gao, Guozhu
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Spline Approximations for Neutral Functional Differential Equations

SIAM Journal on Numerical Analysis, 1981
Based on an abstract approximation theorem for ${\text{C}}_0 $-semigroups (Trotter–Kato theorem) we present an algorithm where linear autonomous functional-differential equations of neutral type are approximated by sequences of ordinary differential equations of increasing dimensions.
Kappel, F., Kunisch, K.
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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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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
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