共查询到20条相似文献,搜索用时 15 毫秒
1.
Thieu Huy Nguyen 《Journal of Mathematical Analysis and Applications》2009,354(1):372-1106
Consider an evolution family U=(U(t,s))t?s?0 on a half-line R+ and a semi-linear integral equation . We prove the existence of stable manifolds of solutions to this equation in the case that (U(t,s))t?s?0 has an exponential dichotomy and the nonlinear forcing term f(t,x) satisfies the non-uniform Lipschitz conditions: ‖f(t,x1)−f(t,x2)‖?φ(t)‖x1−x2‖ for φ being a real and positive function which belongs to admissible function spaces which contain wide classes of function spaces like function spaces of Lp type, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory. 相似文献
2.
3.
Bogdan Sasu 《Journal of Mathematical Analysis and Applications》2006,323(2):1465-1478
The aim of this paper is to give characterizations for uniform and exponential dichotomies of evolution families on the half-line. We associate with a discrete evolution family Φ={Φ(m,n)}(m,n)∈Δ the subspace . Supposing that X1 is closed and complemented, we prove that the admissibility of the pair implies the uniform dichotomy of Φ. Under the same hypothesis on X1, we obtain that the admissibility of the pair with p∈(1,∞] is a sufficient condition for the exponential dichotomy of Φ, which becomes necessary when Φ is with exponential growth. We apply our results in order to deduce new characterizations for exponential dichotomy of evolution families in terms of the solvability of associated difference and integral equations. 相似文献
4.
Nguyen Thieu Huy 《Journal of Differential Equations》2009,246(5):1820-1106
Consider an evolution family U=(U(t,s))t?s?0 on a half-line R+ and a semi-linear integral equation . We prove the existence of invariant manifolds of this equation. These manifolds are constituted by trajectories of the solutions belonging to admissible function spaces which contain wide classes of function spaces like function spaces of Lp type, the Lorentz spaces Lp,q and many other function spaces occurring in interpolation theory. The existence of such manifolds is obtained in the case that (U(t,s))t?s?0 has an exponential dichotomy and the nonlinear forcing term f(t,x) satisfies the non-uniform Lipschitz conditions: ‖f(t,x1)−f(t,x2)‖?φ(t)‖x1−x2‖ for φ being a real and positive function which belongs to certain classes of admissible function spaces. 相似文献
5.
Adina Lumini?a Sasu 《Journal of Mathematical Analysis and Applications》2008,344(2):906-920
The aim of this paper is to provide a new approach concerning the characterization of exponential dichotomy of difference equations by means of admissible pair of sequence spaces. We classify the classes of input and output spaces, respectively, and deduce necessary and sufficient conditions for exponential dichotomy applicable for a large variety of systems. By an example we show that the obtained results are the most general in this topic. As an application we deduce a general lower bound for the dichotomy radius of difference equations in terms of input-output operators acting on sequence spaces which are invariant under translations. 相似文献
6.
For a delay difference equation
7.
Liviu Horia Popescu 《Journal of Mathematical Analysis and Applications》2006,314(2):436-454
In the present paper we extend existing results on exponential dichotomy roughness for linear ODE systems to infinite dimensional Banach space. We give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case. We also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation. 相似文献
8.
Ciprian Preda 《Journal of Mathematical Analysis and Applications》2007,332(1):727-734
Following the Perron-Ta Li line of results, we give a characterization of the uniform exponential dichotomy property for the abstract continuous-time evolution families using a discrete-time approach. 相似文献
9.
Nguyen Thieu Huy 《Journal of Mathematical Analysis and Applications》2004,289(1):301-316
To a backward evolution family on a Banach space X we associate an abstract differential operator G through the integral equation on a Banach space of X-valued functions on . We compute the resolvent of the restriction of this operator to a smaller domain to obtain a generator. We then apply the results to prove existence, exponential stability and exponential dichotomy of solutions to partial functional equations with nonautonomous past as discussed in [S. Brendle, R. Nagel, Dist. Contin. Dynam. Systems 8 (2002) 953-966]. Our main tools are spectral mapping theorems for evolution semigroups and hyperbolicity criteria. 相似文献
10.
Hui-Sheng Ding Wei Long Gaston M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4158-4164
In this paper, we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u′(t)=A(t)u(t)+f(t) and u′(t)=A(t)u(t)+f(t,u(t)) in Banach spaces. As we will see, our results allow for a more general A(t) to some extent. An example is also given to illustrate our results. In addition, by means of an example, we show that one cannot ensure the existence of almost automorphic solutions to u′(t)=A(t)u(t)+f(t) even if the evolution family U(t,s) generated by A(t) is exponentially stable and fAA(X). 相似文献
11.
The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families
on the real line. We prove that if p ∈ (1,∞) and the pair (Cb(R,X),Cc(R,X)) is uniformly p-admissible for an evolution family ={U(t,s)}t≥s then is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (Cb(R, X), Cc(R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform
exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (Cb(R,X),Lp(R,X)) for an evolution family ={U(t,s)}t≥s is equivalent with its uniform exponential dichotomy. 相似文献
12.
Nguyen Thieu Huy 《Journal of Mathematical Analysis and Applications》2007,333(2):731-752
In this paper we investigate the exponential dichotomy of linear skew-product semiflows over semiflows by considering the operators generated by the integral equation related to strongly continuous cocycles over metric spaces acting on Banach bundles. We characterize the existence of exponential dichotomy by properties of these operators and use this characterization to prove the robustness of exponential dichotomy. 相似文献
13.
Fernando Cardoso 《Journal of Difference Equations and Applications》2013,19(3):261-290
We characterize the exponential dichotomy of difference equations with infinite delay. We apply the results to study the robustness of exponential dichotomy. This kind of dichotomy gives us relevant information about boundedness of solutions for several perturbed quasi linear systems with infinite delay. Applications to Volterra difference equations are shown. 相似文献
14.
Liviu Horia Popescu 《Journal of Differential Equations》2004,203(1):28-37
In the present work, we give necessary and sufficient conditions for linear differential non-autonomous equations on a Banach space, that satisfy exponential dichotomy, to be topologically equivalent. We shall also prove that such equations are structurally stable. 相似文献
15.
16.
Tingxiu Wang 《Journal of Mathematical Analysis and Applications》2006,324(2):982-991
With the Lyapunov second method, we study the abstract functional differential equation, . We obtain inequalities of solutions and exponential stability with conditions like:
- (i)
- ,
- (ii)
- .
17.
The paper is concerned with the existence of almost periodic solutions to the so-called semilinear thermoelastic plate systems. For that, the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations
(*) 相似文献
18.
Nguyen Van Minh Frank Räbiger Roland Schnaubelt 《Integral Equations and Operator Theory》1998,32(3):332-353
LetU=(U(t, s))
tsO
be an evolution family on the half-line of bounded linear operators on a Banach spaceX. We introduce operatorsG
O,G
X
andI
X
on certain spaces ofX-valued continuous functions connected with the integral equation
, and we characterize exponential stability, exponential expansiveness and exponential dichotomy ofU by properties ofG
O,G
X
andI
X
, respectively. This extends related results known for finite dimensional spaces and for evolution families on the whole line, respectively.This work was done while the first author was visiting the Department of Mathematics of the University of Tübingen. The support of the Alexander von Humboldt Foundation is gratefully acknowledged. The author wishes to thank R. Nagel and the Functional Analysis group in Tübingen for their kind hospitality and constant encouragement.Support by Deutsche Forschungsgemeinschaft DFG is gratefully acknowledged. 相似文献
19.
The purpose of this paper is to establish the exponential decay properties of the solutions for the nonlinear multiharmonic equation where the condition plays the role of a boundary value condition. 相似文献
20.
Hui-Sheng Ding Jin Liang Gaston M. N’Guérékata Ti-Jun Xiao 《Nonlinear Analysis: Theory, Methods & Applications》2007
This paper is concerned with pseudo-almost periodicity of the solutions to the nonautonomous evolution equation with delay u′(t)=A(t)u(t)+f(t,u(t−h)). Some sufficient conditions which ensure the existence and uniqueness of pseudo-almost periodic mild solutions to the evolution equation with delay are given. An example is shown to illustrate our results. 相似文献