共查询到20条相似文献,搜索用时 15 毫秒
1.
S. Zaidman 《Annali dell'Universita di Ferrara》1969,14(1):101-104
Summary For some differential equations in Hilbert space we prove uniqueness of bounded solutions in the Stepanoff norm.
This research is supported by a grant of the N.R.C. of Canada. 相似文献
Riassunto Si dimostra l’unicità delle soluzioniS 2-limitate per alcune equazioni differenziali astratte.
This research is supported by a grant of the N.R.C. of Canada. 相似文献
2.
Jerome A. Goldstein 《Annali dell'Universita di Ferrara》1971,16(1):39-43
Summary We construct nontrivial bounded solutions of an abstract evolution equationu'(t)=Au(t) (—∞<t<∞) whereA generates a (C
0) semigroup of operators {T
t;t≥0} such thatT
t converges strongly to zero ast→∞.
Supported by National Science Foundation grant GP-12722. 相似文献
Riassunto Si costruiscono soluzioni limitate non triviali di una equazioneu'(t)=Au(t) (—∞<t<∞) doveA è il generatore di un semigruppo di operatori {T t;t≥0} tale cheT t converge fortemente verso 0 pert→∞.
Supported by National Science Foundation grant GP-12722. 相似文献
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Samuel Zaidman 《Annali dell'Universita di Ferrara》1976,22(1):43-47
Summary The paper is concerned with bounded solutions of an equationu′(t)=Bu(t) in Hilbert spaces,
. A representation formula is obtained depending on the zeros of Rez(θ).
This research is supported through a grant of the National Research Council Canada. 相似文献
Riassunto è studiata la struttura delle soluzioni limitate di una equazione differenzialeu′(t)=Bu(t) in uno spazio di Hilbert, ove , in funzione dei zeri di Rez(θ).
This research is supported through a grant of the National Research Council Canada. 相似文献
5.
We prove that if u is a weak solution of the d dimensional fractional Navier-Stokes equations for some initial data u0and if u belongs to path space p = L q ( 0 , T ; B p , ∞ r ) o r p = L 1 ( 0 , T ; B ∞ , ∞ r ) , then u is unique in the class of weak solutions when α>1. The main tools are Bony decomposition and Fourier localization technique. The results generalize and improve many recent known results. 相似文献
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Carlos Lizama 《Applicable analysis》2013,92(8):1731-1754
We propose a unified functional analytic approach to derive a variation of constants formula for a wide class of fractional differential equations using results on (a,?k)-regularized families of bounded and linear operators, which covers as particular cases the theories of C 0-semigroups and cosine families. Using this approach we study the existence of mild solutions to fractional differential equation with nonlocal conditions. We also investigate the asymptotic behaviour of mild solutions to abstract composite fractional relaxation equations. We include in our analysis the Basset and Bagley–Torvik equations. 相似文献
8.
Eduardo Hernández 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2210-2218
We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. 相似文献
9.
Emil Vitásek 《Applications of Mathematics》2007,52(2):171-183
The methods of arbitrarily high orders of accuracy for the solution of an abstract ordinary differential equation are studied.
The right-hand side of the differential equation under investigation contains an unbounded operator which is an infinitesimal
generator of a strongly continuous semigroup of operators. Necessary and sufficient conditions are found for a rational function
to approximate the given semigroup with high accuracy.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. 相似文献
10.
Bogachev V. I.; Da Prato G.; Rockner M.; Stannat W. 《Bulletin London Mathematical Society》2007,39(4):631-640
We study uniqueness of solutions of parabolic equations formeasures µ(dt dx) = µt(dx)dt of the type L*µ = 0, satisfying µt as t 0, where each µtis a probability measure on d, L = t + aij(t, x)xixj + bi(t,x)xj is a differential operator on (0, T) x d and is a giveninitial measure. One main result is that uniqueness holds underuniform ellipticity and Lipschitz conditions on aij but forbi merely local integrability and coercivity conditions aresufficient. 相似文献
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Behavior of bounded solutions for some almost periodic neutral partial functional differential equations 下载免费PDF全文
El Hadi Ait Dads Brahim Es‐sebbar Khalil Ezzinbi Mohamed Ziat 《Mathematical Methods in the Applied Sciences》2017,40(7):2377-2397
We establish a Bochner type characterization for Stepanov almost periodic functions, and we prove a new result about the integration of almost periodic functions. This result is then used together with a reduction principle to investigate the nature of bounded solutions of some almost periodic partial neutral functional differential equations. More specifically, we prove that all bounded solutions on are almost periodic. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
Gani Tr. Stamov 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2457-2464
This paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in Banach space. The investigations are carried out by means of the fractional powers of operators. We construct an example to illustrate the feasibility of our results. 相似文献
15.
Eduardo Hernández 《Mathematical and Computer Modelling》2011,53(1-2):196-204
We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. 相似文献
16.
Eduardo V. Teixeira 《Journal of Differential Equations》2005,214(1):65-91
Let (E,F) be a locally convex space. We denote the bounded elements of E by . In this paper, we prove that if BEb is relatively compact with respect to the F topology and f:I×Eb→Eb is a measurable family of F-continuous maps then for each x0∈Eb there exists a norm-differentiable, (i.e. differentiable with respect to the ∥·∥F norm) local solution to the initial valued problem ut(t)=f(t,u(t)), u(t0)=x0. All of this machinery is developed to study the Lipschitz stability of a nonlinear differential equation involving the Hardy-Littlewood maximal operator. 相似文献
17.
Yoshiyuki Hino 《Journal of Mathematical Analysis and Applications》2003,286(2):741-752
For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. 相似文献
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Sadek Gala 《Applications of Mathematics》2008,53(6):561-582
Consider the Navier-Stokes equation with the initial data a ∈ L
σ
2(ℝ
d
). Let u and v be two weak solutions with the same initial value a. If u satisfies the usual energy inequality and if ∇v ∈ L
2((0, T); (ℝ
d
)
d
) where (ℝ
d
) is the multiplier space, then we have u = v. 相似文献