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71.
Vincenzo Recupero 《Mathematical Methods in the Applied Sciences》2008,31(11):1283-1295
The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data, the existence of solutions is easily obtained from general results on maximal monotone operators. If the datum is a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of the play operator on rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
72.
Keiji Izuchi Shû ichi Ohno 《Proceedings of the American Mathematical Society》2006,134(5):1359-1364
We study Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators are related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras.
73.
Alain Haraux 《Journal of Dynamics and Differential Equations》2007,19(4):915-933
Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A
* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A
1/2) et λ, c sont des constantes positives, tandis que .
By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A
* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A
1/2) and λ, c are positive constants, while .
相似文献
74.
Assume X is a normed space,every x * ∈ S(X*) can reach its norm at some point in B(X),and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L(X,Y) contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L(X,Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X,Y). 相似文献
75.
In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property (u) in substitution spaces are obtained. 相似文献
76.
This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r*which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions(u(ξ), H(ξ)). Furthermore,by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions. 相似文献
77.
Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator. 相似文献
78.
In this paper, we construct a new Roper-Suffridge extension operator Φr n,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)β1z1,(rf(z1/r)/z1)β2z2,...,(rf(z1/r)/z1)βnzn)',where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, ···, zn) ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively. 相似文献
79.
The aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces. For this purpose we take advantage of the basic fact that the space Pm(E) of all m-homogeneous polynomials on a vector space E can be identified with the algebraic dual of the m -th symmetric tensor product ⊗m,sE. Given an operator space V, we study several different types of completely bounded polynomials on V which form the operator space duals of ⊗m,sV endowed with related operator structures. Of special interest are what we call Haagerup, Kronecker, and Schur polynomials – polynomials associated with different types of matrix products. 相似文献
80.
We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces c0 and ?1 has a subspace which has the AP but fails to have the strong AP. 相似文献