Results 261 to 270 of about 428,756 (295)

Impulsive Semi-linear Functional Differential Equations

2015
In this chapter, we shall prove the existence of mild solutions of first order impulsive functional equations in a separable Banach space. Our approach will be based for the existence of mild solutions, on a fixed point theorem of Burton and Kirk [88] for the sum of a contraction map and a completely continuous map.
Saïd Abbas, Mouffak Benchohra
openaire   +1 more source

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
openaire   +2 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.
openaire   +2 more sources

Linear Functional Differential Equations as Semigroups on Product Spaces

SIAM Journal on Mathematical Analysis, 1983
In this paper we consider the well-posedness of linear functional differential equations on product spaces. Let L and D be linear $\mathbb{R}^n $-valued functions with domains $\mathfrak{D}(L)$ and $\mathfrak{D}(D)$ subspaces of the Lebesgue measurable $\mathbb{R}^n $-valued functions on $[ - r,0]$ and such that $W^{1,p} ([ - r,0];\mathbb{R}^n ...
Burns, John A., Herdman, Terry L., Stech, Harlan W.   +2 more
openaire   +2 more sources

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.
openaire   +2 more sources

Slowly varying, linear, neutral, functional, differential equations†

International Journal of Control, 1973
Abstract For a slowly varying, linear, neutral, functional, differential equation, a sufficient condition is derived which ensures uniform exponential stability.
openaire   +1 more source

Linear measure functional differential equations with infinite delay

Mathematische Nachrichten, 2014
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions.
Monteiro, G. (Giselle Antunes), Slavík, A.   +1 more
openaire   +3 more sources

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 ...
openaire   +2 more sources

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.
openaire   +2 more sources

One class of singular linear functional differential equations

Russian Mathematics, 2012
Consider the functional differential equation \[ x'(t)+ a(t)x(t) +(Tx)(t) = f(t), 0\leq t\leq b, \] where \(a(t)\) has the form \(a(t) = \frac{k}{t} + \tilde{a}(t)\) with certain conditions, and the linear operator \(T\) from the space of absolutely continuous functions on \([0, b]\) to the Banach space \(L^p[0, b]\) is completely continuous ...
openaire   +2 more sources