Results 291 to 300 of about 257,023 (328)

Continuity in functional differential equations with infinite delay

Acta Mathematicae Applicatae Sinica, 1991
A continuity approach is presented for the equation (1) \(\dot x=f(t,x_ t)\) with infinite delay, where the function \(f\) satisfies a so-called fading memory condition. The space \(X\) of the initial functions is endowed with two topologies (the sup-norm topology and a \(g\)-norm topology). The authors investigate when (i) continuity of the solution \(
T. A. Burton, Feng Youhe
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Retarded equations with infinite delays

1979
It is the purpose of these notes to describe the theory of Hale and Kato for functional differential equations based on a space of initial data which satisfy some very reasonable axioms. We also indicate some recent results of Naito showing how extensive the theory of linear systems can be developed in an abstract setting in particular, the ...
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On small solutions of delay equations in infinite dimensions

Integral Equations and Operator Theory, 1998
The problem under consideration is the delay differential equation \(\dot u(t) = Lu_t, u(0)=x, u_0 =f\), in the state space \(L^p ([-1,0], X)\), with \(1\leq ...
S. Z. Huang, J. M. A. M. van Neerven
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The stability of motions of hereditary systems with infinite delay [PDF]

Doklady Mathematics, 2007
Several conditions for the stability of equalibria and stationary motions of hereditary mechanical systems with infinite delayhas been identified. The system of functional-differential equations with infinite delay was considered where a continuous mapping exists satisfying the conditions for the existence and uniqueness of a solution at each point ...
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On a periodic prey-predator system with infinite delays

Applied Mathematics-A Journal of Chinese Universities, 2000
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Xu Guitong, Li Yongkun
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Boundedness of infinite delay difference systems

Nonlinear Analysis: Theory, Methods & Applications, 1994
Recently the author has obtained stability results for the infinite delay difference system \(x(n+1) = G(n,x(s);s\;l,l + 1,\dots,n)\) [Stability of infinite delay difference systems. Nonlinear Anal. Theory Methods Appl. 22, No. 9, 1121-1129 (1994)]. In this paper some theorems on boundedness are established.
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Stability of functional differential equations with infinite delays

Applied Mathematics-A Journal of Chinese Universities, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luo Zhi-guo, Shen Jian-hua
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Stability of infinite delay difference systems

Nonlinear Analysis: Theory, Methods & Applications, 1994
The author considers general delay difference systems with infinite delay of the form \[ x(n+ 1)= G(n, x(s);\;s= l,l+1,\dots, n)=: G(n, x(\cdot)), \tag{*} \] where \(l\) is an integer or \(-\infty\). It is assumed that \(G(n, 0)\equiv 0\) for \(n= l, l+1,\dots\), so that \((*)\) has the zero solution \(x(n)\equiv 0\).
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On Oscillation of a Differential Equation with Infinite Number of Delays

Zeitschrift für Analysis und ihre Anwendungen, 2002
For a scalar delay differential equation \dot{x}(t) + \sum^\infty_{k=1} a_k(t)x(h_k(t)) = 0 \; \; \; (H_k(t) ≤ t) a connection between the following four properties is established:
Leonid Berezansky, Elena Braverman
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Stability and Boundedness for Equations with Infinite Delay

1994
This chapter is devoted to the investigation of stability and boundedness results of equations with infinite memory. We shall first discuss, in Sections 6.1 to 6.3, FDE with infinite delay and develop, in the general setup of two different measures, criteria for stability and boundedness.
V. Lakshmikantham, Binggen Zhang, Lizhi Wen   +2 more
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