共查询到20条相似文献,搜索用时 15 毫秒
1.
András Bátkai 《Integral Equations and Operator Theory》2002,44(4):383-396
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.The author thanks W. Desch (Graz), I. Gyri (Veszprém) and R. Schnaubelt (Halle) for helpful discussions. 相似文献
2.
LetX be a Banach space and 1p<. LetL be a bounded linear operator fromL
p
([–1,0],X) intoX. Consider the delay differential equationu(t)=Lu
t
,u(0)=x,u
0=f on the state spaceL
p
([–1,0],X). We prove that a mild solutionu(t)=u(t;x,f) is a small solution if and only if the Laplace transform ofu(t;x,f) extends to an entire function. The same result holds for the state spaceC([–1,0],X).This paper was written while the authors were affiliated with the University of Tübingen. It is part of a research project supported by the Deutsche Forschungsgemeinschaft DFG. The authors warmly thank Professor Rainer Nagel and the AG Funktionalanalysis for the stimulating and enjoyable working environment.Support by DAAD is gratefully acknowledged.Support by an Individual Fellowship from the Human Capital and Mobility programme of the European Community is gratefully acknowledged. 相似文献
3.
Verónica Poblete 《Journal of Differential Equations》2009,246(1):261-1037
We characterize existence and uniqueness of solutions of an inhomogeneous abstract delay equation in Hölder spaces. The method is based on the theory of operator-valued Fourier multipliers. 相似文献
4.
In this paper we study C0-semigroups on X × Lp( − h, 0; X) associated with linear differential equations with delay, where X is a Banach space. In the case that X is a Banach lattice with order continuous norm, we describe the associated modulus semigroup, under minimal assumptions on
the delay operator. Moreover, we present a new class of delay operators for which the delay equation is well-posed for p in a subinterval of [1,∞).
Dedicated to the memory of H. H. Schaefer 相似文献
6.
Eduardo Hernández Jair Silvério dos Santos Katia A.G. Azevedo 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2624-2634
We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. 相似文献
7.
Genni Fragnelli 《Archiv der Mathematik》2002,79(6):479-488
We study partial functional differential equations with infinite delay where the history function is modified by a backward
evolution family. Under appropriate assumptions and using semigroup techniques we prove the existence of a unique classical
solution.
Die endgültige Fassung ging am 20. 6. 2001 einein 相似文献
8.
C. J. K. Batty 《Archiv der Mathematik》2003,81(1):72-81
Let $f : \mathbb{R}_{+} \rightarrow \mathbb{C}$ be an exponentially bounded,
measurable function whose Laplace transform has a bounded holomorphic
extension to the open right half-plane. It is known that there is a
constant C such that $\mid \int\limits^t_0 f(s) ds \mid\, \leq C (1 + t)$
for all $t \geq 0$. We show that this estimate is sharp. Furthermore, the
corresponding estimates for orbits of $C_0$-semigroups are also sharp.
Received:17 January 2001; revised manuscropt accepted: 8 February 2001 相似文献
9.
10.
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to that of the corresponding deterministic delay differential equation. However, boundedness of the second moment is complicated and depends on the stochastic terms. In this paper, the characteristic function of the equation is obtained through techniques of the Laplace transform. From the characteristic equation, sufficient conditions for the second moment to be bounded or unbounded are proposed. 相似文献
11.
Let Ω be an exterior domain in
It is shown that Ornstein-Uhlenbeck operators L generate C0-semigroups on Lp(Ω) for p ∈ (1, ∞) provided ∂Ω is smooth. The method presented also allows to determine the domain D(L) of L and to prove Lp − Lq smoothing properties of etL. If ∂Ω is only Lipschitz, results of this type are shown to be true for p close to 2.
Received: 16 December 2004; revised: 4 February 2005 相似文献
12.
《Quaestiones Mathematicae》2013,36(8):1073-1082
AbstractIn this paper we study a two-phase population model, which distinguishes the population by two different stagesBy the standard technique of characteristics, this population equation is transformed as the ordinary differential equation with nonautonomous pastwhere 1 ≤ p < ∞ and I = [?r, 0] (finite delay) or I = (?∞, 0] (infinite delay), E a Banach space, Φ : W1,p(I, E) → E a linear delay operator and B a nonlinear operator on E. The main result of this paper is the well-posedness of this delay equation by using the (right) multiplicative perturbation result of Desch and Schappacher in [8]. 相似文献
13.
It is shown that there cannot exist a uniform exponential dichotomy for any linear delay equation with a positive finite delay. 相似文献
14.
Manuel Pinto 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4377-4383
The existence and uniqueness of pseudo-almost periodic solutions to general neutral integral equations with deviations are obtained. For this, pseudo-almost periodic functions in two variables are considered. The results extend the corresponding ones to the convolution type integral equations. They are used to study pseudo-almost periodic solutions of general neutral differential equations and to the so-called scalar neutral logistic equation version. 相似文献
15.
Existence of solutions for impulsive partial neutral functional differential equation with infinite delay 总被引:1,自引:0,他引:1
Runping Ye 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(1):155-162
In this paper, the existence of mild solutions for first-order impulsive semilinear neutral functional differential equations with infinite delay in Banach spaces is investigated. We derive conditions in respect of the Hausdorff measure of noncompactness under which the mild solutions exist in Banach spaces. Our results improve and generalize some previous results. 相似文献
16.
Marco Romito 《Monatshefte für Mathematik》1998,126(4):329-352
Given an open bounded convex subset of
p
, a strictly elliptic differential operatorL and a continuous function
, and denoted withT
L the Dirichlet operator associated withL, the Lototsky-Schnabl operators associated withT
L and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.Work supported by a C.N.R. Research Grant (n. 201.19.1, November 30, 1994) 相似文献
17.
Eduardo Hernández Michelle Pierri 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3633-3643
By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. 相似文献
18.
19.
H. R. Henriquez 《Acta Mathematica Hungarica》2008,121(3):203-227
We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous
neutral functional differential equations with infinite delay in a Banach space.
This research was supported by FONDECYT-CONICYT, Grant 1050314. 相似文献
20.
Pascale Vitse 《Archiv der Mathematik》2005,85(4):374-385
For Banach space operators T satisfying the Tadmor-Ritt condition
a band limited H∞ calculus is established,
where
and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus,
These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived.
Received: 25 October 2004; revised: 31 January 2005 相似文献