共查询到18条相似文献,搜索用时 0 毫秒
1.
Connections between uniform exponential expansiveness and complete admissibility of the pair
are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given. 相似文献
2.
On the Stability of Functional Equations and a Problem of Ulam 总被引:10,自引:0,他引:10
Themistocles M. Rassias 《Acta Appl Math》2000,62(1):23-130
In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory. 相似文献
3.
Kil-Woung Jun 《Journal of Mathematical Analysis and Applications》2005,312(2):535-547
Let G1 be a vector space and G2 a Banach space. In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for a generalized form
4.
Let {T(t)}t≥0 be a C0–semigroup on a Banach space X with generator A, and let H∞T be the space of all x ∈ X such that the local resolvent λ ↦ R(λ, A)x has a bounded holomorphic extension to the right half–plane. For the class of integrable functions ϕ on [0, ∞) whose Fourier transforms are integrable, we construct a functional calculus ϕ ↦ Tϕ, as operators on H∞T. Weshow that each orbit T(·)Tϕx is bounded and uniformly continuous, and T(t)Tϕx → 0 weakly as t → ∞, and we give a new proof that ∥T(t)R(μ, A)x∥ = O(t). We also show that ∥T(t)Tϕx∥ → 0 when T is sun –reflexive, and that ∥T(t)R(μ, A)x∥ = O(ln t) when T is a positive semigroup on a normal ordered space X and x is a positive vector in H∞T. 相似文献
5.
This paper is devoted to the well-posedness of abstract Cauchyproblems for quasi-linear evolution equations. The notion ofHadamard well-posedness is considered, and a new type of stabilitycondition is introduced from the viewpoint of the theory offinite difference approximations. The result obtained here generalizesnot only some results on abstract Cauchy problems closely relatedwith the theory of integrated semigroups or regularized semigroupsbut also the Kato theorem on quasi-linear evolution equations.An application to some quasi-linear partial differential equationof weakly hyperbolic type is also given. 2000 Mathematics SubjectClassification 34G20, 47J25 (primary), 47D60, 47D62 (secondary). 相似文献
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郑州工程学院数理系 《数学物理学报(A辑)》2004,24(3):329-336
该文考虑一类新的非线性方程(|ut|r-2ut)t-Δutt-Δu-ρ(t)Δut=f(u) 的初边值问题,利用小扰动法证明了整体弱解的
存在性,借用位势井的概念得到了解的稳定性.〖HT5”H〗关键词:〖HT5”SS〗非线性发展方程;初边值问题;整体弱解;稳定性. 相似文献
9.
Necessary and also sufficient monodromy conditions for a large class of degenerate singular points of planar differential systems are given. For these systems, we also find a computable expression of the principal term of the asymptotic expansion of the return map, which gives the stability of the point. 相似文献
10.
Hong-jiong Tian 《计算数学(英文版)》2003,21(6):715-726
This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1. 相似文献
11.
Vinod Sharma 《Queueing Systems》1994,16(1-2):115-137
The stability of a polling system with exhaustive service and a finite number of users, each with infinite buffers is considered. The arrival process is more general than a Poisson process and the system is not slotted. Stochastic continuity of the stationary distributions, rates of convergence and functional limit theorems for the queue length and waiting time processes have also been proved. The results extend to the gated service discipline. 相似文献
12.
Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line 下载免费PDF全文
Hai-Liang Li & Shuang Zhao 《数学研究通讯:英文版》2020,36(4):423-459
The outflow problem for the viscous two-phase flow model in a half
line is investigated in the present paper. The existence and uniqueness of the
stationary solution is shown for both supersonic state and sonic state at spatial
far field, and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay
rate for supersonic flow or the algebraic time decay rate for sonic flow. 相似文献
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14.
Charles J. K. Batty Jan van Neerven Frank Rä biger 《Transactions of the American Mathematical Society》1998,350(5):2087-2103
Let be a bounded, strongly measurable function with values in a Banach space , and let be the singular set of the Laplace transform in . Suppose that is countable and uniformly for , as , for each in . It is shown that
as , for each in ; in particular, if is uniformly continuous. This result is similar to a Tauberian theorem of Arendt and Batty. It is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on , and it implies several results concerning stability of solutions of Cauchy problems.
15.
研究了具有时滞和Beddington-DeAngelis功能反应的一类食物链系统,通过运用Mawhin重合度理论中的延拓定理,得到了系统至少存在一个周期解的充分条件,并通过构造Lyapunov泛函的方法得到了系统周期解的全局稳定性. 相似文献
16.
Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces 下载免费PDF全文
In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of $2$ is less than $1$ cannot be omitted in our corollaries. The results improve and extend some recent results. 相似文献
17.
In this paper we study R-boundedness of operator families , where X and Y are Banach spaces. Under cotype and type assumptions on X and Y we give sufficient conditions for R-boundedness. In the first part we show that certain integral operator are R-bounded. This will be used to obtain R-boundedness in the case that is the range of an operator-valued function which is in a certain Besov space . The results will be applied to obtain R-boundedness of semigroups and evolution families, and to obtain sufficient conditions for existence of solutions for stochastic
Cauchy problems.
Mark Veraar is supported by the Alexander von Humboldt foundation. His visit to Helsinki, which started this project, was
funded by the Finnish Centre of Excellence in Analysis and Dynamics Research. 相似文献
18.
In this paper, a stochastic SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. The model inherits the endemic steady state from its corresponding deterministic counterpart. We first show the existence and uniqueness of the global positive solution of the model. Then, by constructing Lyapunov functionals, we derive sufficient conditions ensuring the stochastic stability of the endemic steady state. Numerical simulations are carried out to confirm our analytical results. Furthermore, our simulation results shows that the existence of noise and delay may cause the endemic steady state to be unstable. 相似文献