Results 271 to 280 of about 89,989 (306)

L p -Perturbation of Linear Functional Differential Equations

Monatshefte f�r Mathematik, 1999
Here, it is shown that a certain class of retarded linear differential equations with solutions of exponential form is stable under \(L^{p}\)-perturbations. An example illustrating this result is given. As a particular case, the asymptotic integration of a class of delay equations of the form \({x'(t)=\sum_{k=0}^{k}}(a_{k}+q_{k}(t))x(t-k\tau)\) is ...
Cassell, J. S., Hou, Zhanyuan
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Linearized Stability and Irreducibility for a Functional Differential Equation

SIAM Journal on Mathematical Analysis, 1992
For a Banach space valued nonlinear functional differential equation the author develops a principle of linearized stability. Following ideas of \textit{A. Grabosch} [Trans. Am. Math. Soc. 311, No. 1, 357-390 (1989; Zbl 0675.47037)] positivity assumptions on this linearization are used in order to obtain simple stability criteria.
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Large Time Behaviour of Linear Functional Differential Equations

Integral Equations and Operator Theory, 2003
The authors consider linear autonomous functional-differential equations of the type \[ {d\over dt} Dx_t= Lx_t,\quad t\geq 0,\quad x_0= \phi, \] with \(x_t(\theta)= x(t+ \theta)\), \(-r\leq\theta\leq 0\), \[ L\phi= \int^0_{-r} d\eta(\theta\phi(\theta),\quad D\phi= \phi(0)- \int^0_{-r} d\mu(\theta)\phi(\theta). \] Here, \(\theta\), \(\mu\) are \(n\times
Frasson, Miguel V. S., Verduyn Lunel, Sjoerd M.   +1 more
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Linear Functional-Differential Equations with Absolutely Unstable Solutions

Ukrainian Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear Functional-Differential Equations in a Banach Algebra^*

Canadian Mathematical Bulletin, 1978
The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting.
Fitzpatrick, W. J., Grimm, L. J.
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Approximation of Eigenvalues of Evolution Operators for Linear Retarded Functional Differential Equations

SIAM Journal on Numerical Analysis, 2012
This paper deals with the approximation of the eigenvalues of evolution operators for linear retarded functional differential equations through the reduction to finite dimensional operators by a pseudospectral collocation. Fundamental applications such as determination of asymptotic stability of equilibria and periodic solutions of nonlinear autonomous
Dimitri Breda, S Maset, Rossana Vermiglio   +2 more
exaly   +4 more sources

Decomposition of linear singularly perturbed functional-differential equations

2021
The authors consider the system of functional-differential equations \[ \begin{alignedat}{3} \frac{dx}{dt}&= L_0x_t + L_1(t)x_t + L_2(t) y_t, &\quad x_t(0)&= \varphi(\theta), &\quad &\theta\in [-\Delta,0],\\ \varepsilon\,\frac{dy}{dt}&=L_3(t)y_t + L_4(t)x_t, &\quad y_t(0)&= \psi(\theta), &\quad &\theta\in [-\varepsilon\Delta,0], \end{alignedat ...
Perestyuk, M.O., Cherevko, I.M.
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On Reducible Linear Functional Differential Equations of Mixed Type

Mathematische Nachrichten, 2000
Consider the linear autonomous FDE of mixed type \({d\over dt} (Dx_t)=Lx_t\), with \(x_t(\theta)= x(t+\theta)\), \(\theta\in [-r,\rho]\), \(r>0\), \(\rho>0\) and \(D,L\) are bounded linear mappings from \(C([-r,\rho],C^N)\) to \(C^N\), given by \[ D\varphi= \varphi(0)-\int^0_{-r} \varphi(\theta) ds(\theta),\;L\varphi= \int^\rho_{-r}\varphi (\theta)d ...
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Stability for abstract linear functional differential equations

Israel Journal of Mathematics, 1985
The paper deals with the initial value problem \[ (P)\quad \dot u(t)=Au(t)+A_ 1u(t-r)+\int^{0}_{-r}a(s)A_ 2u(t+s)ds+f(t),\quad ...
Di Blasio, G., Kunisch, K., Sinestrari, E.   +2 more
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Non-linear functional differential equations and abstract integral equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1979
SynopsisThe equivalence between solutions of functional differential equations and an abstract integral equation is investigated. Using this result we derive a general approximation result in the state space C and consider as an example approximation by first order spline functions.
Kappel, F., Schappacher, W.
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