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POSITIVE SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Acta Mathematica Scientia, 1996The 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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Oscillation of Neutral Functional Differential Equations
Acta Mathematica Hungarica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Total Stability for Neutral Functional Differential Equations
Proceedings of the American Mathematical Society, 1981The basic idea of this work is to use Lyapunov functionals to show that for neutral functional differential equations, uniform asymptotic stability implies total stability.
Ize, A. F., Freiria, A. A.
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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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Positive periodic solutions for neutral functional differential equations
Applied Mathematics Letters, 2020The present paper applies a fixed point theorem in the cone and some new analysis techniques to establish some sufficient conditions which guarantee the existence of positive periodic solutions for some neutral functional differential equations.
Weibing Wang, Jianhua Shen
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A Neutral Functional Differential Equation of Lurie Type
SIAM Journal on Mathematical Analysis, 1980The 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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Convergence in a system of critical neutral functional differential equations
Applied Mathematics Letters, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoling Zhang, Haijun Hu
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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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Semigroups Generated by a Neutral Functional Differential Equation
SIAM Journal on Mathematical Analysis, 1986We discuss a number of semigroups generated by neutral functional equations of the form \[ d/dt(x(t)+\mu *x(t))+\nu *x(t)=f(t),\quad t\geq 0,\quad x(t)=\phi (t),\quad t\leq 0. \] They are of extended initial function type and of extended forcing function type, and they differ from each other by the amount of smoothness which is imposed on x and f above.
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