Results 271 to 280 of about 76,854 (299)

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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Exact regions of oscillation for a neutral differential equation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
This paper is concerned with a neutral differential equation with four constant coefficients, one delay and one advancement. By means of the theory of envelopes, we consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.
Cheng, S. S., Lin, Y. Z.
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PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Journal of the London Mathematical Society, 2002
The paper concerns the existence, uniqueness and global attractivity of periodic solutions to neutral functional-differential equations with monotone semiflows. The proofs are based on the theory established by Wu and Freedman for monotone semiflow generated by neutral functional-differential equations and Krasnosel'skii's fixed-point theorem.
Wang, Lianglong, Wang, Zhicheng, Zou, Xingfu   +2 more
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Zero-Hopf Calculations for Neutral Differential Equations

Journal of Dynamics and Differential Equations, 2023
The paper focusses on necessary conditions to guarantee the existence of the zero-Hopf singularity for differential equations of neutral type. Consider a neutral functional differential equation \[ \dot{z}(t) +E \dot{z}(t-\tau)= A(\epsilon)z(t)+B(\epsilon)z(t-\tau)+F(z(t),z(t-\tau),\epsilon)\tag{1} \] where \( z\in \mathbb{R}^n, \epsilon \in \mathbb{R}^
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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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A remark on oscillatory results for neutral differential equations

Applied Mathematics Letters, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
George E. Chatzarakis, Jozef Dzurina, Irena Jadlovská   +2 more
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Linearized Oscillations for Differential Equations of Neutral Type

Mathematische Nachrichten, 1995
AbstractAbstract.Consider the nonlinear neutral delay differential equationmagnified imagewithP(t),Q(t) continuous, τ > 0, σ> 0. We obtain new sufficient conditions for the oscillation of all solutions by an associate linear equation, and thereby establish some new criteria as proposed in an earlier open problem.
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Neutral Functional Differential Equations

1999
The present chapter contains some remarks and ideas concerning application of i—smooth calculus to functional differential equations of neutral type. Taking into account essential features of neutral functional differential equations (NFDE) subsequent elaboration of these aspects requires additional investigating properties of invariant differentiable ...
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Positive solutions of neutral delay differential equation [PDF]

, 2002
Let \(I:=[t_0,T ...
Péics Hajnalka, Karsai János
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A Neutral Functional Differential Equation of Lurie Type

SIAM Journal on Mathematical Analysis, 1980
The problem of Lurie is posed for systems described by a functional differential equation of neutral type. Sufficient conditions are obtained for absolute stability for the controlled system if it is assumed that the uncontrolled plant equation is uniformly asymptotically stable. Both the direct and indirect control cases are treated.
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