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1.
2.
Markus Haase 《Journal of Evolution Equations》2007,7(3):529-554
Let –iA be the generator of a C
0-group U on a Banach space X. Via a transference principle we obtain results of the form
for certain functions f, provided that X is a UMD space. Special examples are
The first choice leads to easy proofs of the theorems of Monniaux and Dore–Venni, the second is related to a new proof of
Fattorini’s theorem on cosine functions. 相似文献
3.
C. Buşe A. D. R. Choudary S. S. Dragomir M. S. Prajea 《Integral Equations and Operator Theory》2008,61(3):325-340
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family defined on a Banach space and satisfying some measurability conditions is uniformly exponentially stable if and only if for
some 1 ≤ p < ∞, we have that:
Actually the Barbashin result was formulated for non-autonomous differential equations in the framework of finite dimensional
spaces. Here we replace the above ”uniform” condition be a ”strong” one.
Among others we shall prove that the evolution family is uniformly exponentially stable if there exists a non-decreasing function with for all r > 0 such that for each , one has:
In particular, the family U is uniformly exponentially stable if and only if for some 0 < p < ∞ and each , the inequality
is fulfilled. The latter result extends a similar one from the recent paper [4]. Related results for periodic evolution families
are also obtained.
相似文献
4.
Aleksander Ćwiszewski 《Journal of Evolution Equations》2007,7(1):1-33
In the paper a topological degree is constructed for the class of maps of the form − A + F where M is a closed neighborhood retract in a Banach space
is a m-accretive map such that − A generates a compact semigroup and F : M→ E is a locally Lipschitz map. The obtained degree is applied to studying the existence and branching of periodic points of
differential inclusions of the type
相似文献
5.
Sebastian Król 《Journal of Evolution Equations》2009,9(3):449-468
The concept of the gap function is used to give new perturbation results for generators of holomorphic semigroups. In particular, we show that if A is the generator of a holomorphic semigroup on a Banach space and , then every closed linear operator C such that for some and
generates a holomorphic semigroup, too. Moreover, we obtain an analogue of this result for differences of semigroups. If T is a holomorphic semigroup and , then every C
0-semigroup S with
is holomorphic. We also give certain estimates for the constants M
A
and k
T
appearing in the above conditions.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr N201384834. 相似文献
6.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
, wheref∈L
1
loc(ℝ) is the unknown function andg,T
1, andT
2 are given functions satisfying the conditions
.
Most attention is paid to the nontrivial solvability of the homogeneous equation
.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
7.
In this paper we find a closed form of the solution for the factored inhomogeneous linear equation
Under the hypothesis A
1, A
2, …, A
n
are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach
space X. Here we do not assume that A
j
s are distinct and we offer the computational method to get explicit solutions of certain partial differential equations. 相似文献
8.
This paper deals with the existence of positive solutions for the nonlinear system
. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u
1, …, u
n) and f
i, i = 1, 2, …, n are continuous and nonnegative functions, p(t), q(t): [0, 1] → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for
. The proof is based on a well-known fixed point theorem in cones. 相似文献
9.
Roger Nussbaum 《Integral Equations and Operator Theory》2001,39(1):41-97
LetC(S) denote the Banach space of continuous, real-valued mapsf:S and letA denote a positive linear map ofC(S) into itself. We give necessary conditions that the operatorA have a strictly positive periodic point of minimal periodm. Under mild compactness conditions on the operatorA, we prove that these necessary conditions are also sufficient to guarantee existence of a strictly positive periodic point of minimal periodm. We study a class of Perron-Frobenius operators defined by
and we show how to verify the necessary compactness conditions to apply our theorems concerning existence of positive periodic points.Partially supported by NSF DMS 97-06891 相似文献
10.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
11.
Let A = d/dθ denote the generator of the rotation group in the space C(Γ), where Γ denotes the unit circle. We show that the stochastic Cauchy problem
, where b is a standard Brownian motion and f ∈ C(Γ) is fixed, has a weak solution if and only if the stochastic convolution process t ↦ (f * b)t has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination
with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all f ∈ C(Γ) outside a set of the first category. 相似文献
| ((1)) |
12.
LI Xiong 《中国科学A辑(英文版)》2001,44(2):137-144
We are concerned with the boundedness of all the solutions for second order differential equation
, wheref(x) andg(x) are odd, e( t) is odd and 1-periodic, andg(x) satisfies
相似文献
13.
WUSHAOPING YANGHAITAO 《高校应用数学学报(英文版)》1998,13(3):251-262
Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x f(t,x)=0 are given by means of variational methods, where the function -1/2a（t）|s|^2∫^t0f（t,s）ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t 1 t a（t）dt= ∞,VI∈R^1.A resonance case as well as a noncompact case is discussed too. 相似文献
14.
The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX
On the real line and of
On the half-line are studied. Assuming that the inhomogeneityf (resp.g) belongs to a given homogeneous subspace ofBUC(X) (resp.BUC(
+;X)) it is shown that given bounded solutionsu (resp.v) belong also to provided the spectra of these equations are countable. The results are applied to an equation of scalar type which is of importance in applications like viscoelasticity. 相似文献
15.
Sufficient conditions for the nth order linear differential equation
, to have Property A or Property B are established in both the delayed and the advanced cases. These conditions essentially improve many known results not only for differential equations with deviating arguments but for ordinary differential equations as well. 相似文献
16.
Rumen Tsanev Marinov 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):11-27
In this article, we study an iterative procedure of the following form
, where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations.
We show that this method is locally Q-linearly convergent to a solution x* of the generalized equation
if the set-valued map
is Aubin continuous at (0, x*) with a constant M for growth, f: X → Y is a function, whose Fréchet derivative is L-Lipschitz and A ∈ L(X,Y) is such that 2M∥Δf(x*) − A∥ < 1. We also study the stability of this method.
The research of this paper is partially supported by a Technical University of Varna internal research grant number 487/2008. 相似文献
17.
18.
Qikeng Lu 《中国科学A辑(英文版)》1998,41(12):1248-1254
In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of Cm+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that
is a U(m)-connection of ℱ(m,n) and its curvature form
satisfies the Yang-Mills equation. Moreover,
is an (Sum)-connection and its curvature form
satisfies the Yang-Mills equation.
Project partially supported by the National Natural Science Foundation of China (Grant No. 19631010) and Fundamental Research
Bureau of CAS. 相似文献
19.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
20.
A. K. Tripathy 《Mathematica Slovaca》2008,58(5):581-604
Oscillatory and asymptotic behaviour of solutions of a class of fourth order nonlinear neutral difference equations of the
form
and
are studied under the assumption < ∞, for different ranges of p(n). Sufficient conditions are obtained for the existence of positive bounded solutions of (E).
相似文献