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Perturbed Impulsive Neutral Stochastic Functional Differential Equations
Qualitative Theory of Dynamical Systems, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng, Lijuan, Hu, Lanying, Ren, Yong
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Unstable Neutral Fuctional Differential Equations
Canadian Mathematical Bulletin, 1990AbstractLet y be the solution of the equationwhere A, B, C, λ and η aie complex numbers and It is shown that y has exponential order equal to one if A ≠ 0 and if y is not a polynomial; otherwise, y has exponential order equal to zero. In the latter case, y and all of its derivatives are unbounded on any ray.
Alan Feldstein, Zdzislaw Jackiewicz
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Neutral Differential Equations
2012Chapter 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 +3 more
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Oscillation of Neutral Functional Differential Equations
Acta Mathematica Hungarica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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OSCILLATIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Acta Mathematica Scientia, 1992This 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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Spline Approximations for Neutral Functional Differential Equations
SIAM Journal on Numerical Analysis, 1981Based 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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PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Acta Mathematica Scientia, 2001The 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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LOGISTIC DIFFERENTIAL EQUATION OF NEUTRAL TYPE
1997The 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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Zero-Hopf Calculations for Neutral Differential Equations
Journal of Dynamics and Differential Equations, 2023The 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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Neutral Functional Differential Equations
1999The 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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