共查询到20条相似文献,搜索用时 31 毫秒
1.
Elena Litsyn 《Integral Equations and Operator Theory》2007,58(2):239-253
The new definition of Volterra operator introduced in [5] allows specification of the classical theory of linear equations
in Banach spaces to equations with such operators. Here we specially address relations between properties of the given linear
equation with Volterra operator and properties of its conjugate. As well we treat the theory of Noetherian and Fredholm equations. 相似文献
2.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2007,327(1):257-268
This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties. 相似文献
3.
Dió medes Bá rcenas 《Proceedings of the American Mathematical Society》2000,128(5):1357-1360
By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.
4.
In this paper we consider linear integro-differential equations in Banach spaces with Fredholm operators at the highest-order
derivatives and convolution-type Volterra integral parts. We obtain sufficient conditions for the unique solvability (in the
classical sense) of the Cauchy problem for the mentioned equations and illustrate the abstract results with pithy examples.
The studies are carried out in classes of distributions in Banach spaces with the help of the theory of fundamental operator
functions of degenerate integro-differential operators. We propose a universal technique for proving theorems on the form
of fundamental operator functions. 相似文献
5.
A. V. Chaikovs’kyi 《Ukrainian Mathematical Journal》2011,62(10):1635-1648
We study the representation for functions of shift operator acting upon bounded sequences of elements of a Banach space. An
estimate is obtained for the bounded solution of a linear difference equation in the Banach space. For two types of differential
equations in Banach spaces, we present sufficient conditions for their bounded solutions to be limits of bounded solutions
of the corresponding difference equations and establish estimates for the rate of convergence. 相似文献
6.
Aissa Aibeche Nasreddine Amroune Stephane Maingot 《Mediterranean Journal of Mathematics》2016,13(3):1051-1063
In this work, we give new results concerning existence, uniqueness and maximal regularity of the strict solution of a class of elliptic equations with non-local boundary conditions containing an unbounded linear operator. This study is performed in the framework of UMD Banach spaces. 相似文献
7.
Quan Zheng 《Integral Equations and Operator Theory》1994,19(1):105-119
Corresponding to the strong wellpssedness of the Cauchy problems for complete second order linear differential equations in Banach spaces, we introduce a notion of strongly continuous M, N-families and establish some basic results for these operator families.The project supported by National Science Fundation of China. 相似文献
8.
Miroslaw Lustyk Julian Janus Marzenna Pytel-Kudela Anatoliy K. Prykarpatsky 《Central European Journal of Mathematics》2009,7(4):775-786
The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator
equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating
schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence
theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated
solution sets, based on a Leray-Schauder type fixed point theorem, are obtained. 相似文献
9.
本文讨论了 Banach空间中 Sturm-Liouville问题正解的存在性与多解性,通过线性算子的谱半径,给出其正解存在与多解的条件. 相似文献
10.
Veli Shakhmurov 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2383-2397
This paper focuses on nonlocal boundary value problems for linear and nonlinear abstract elliptic equations in Banach spaces. Here equations and boundary conditions contain certain parameters. The uniform separability of the linear problem and the existence and uniqueness of maximal regular solution of nonlinear problem are obtained in Lp spaces. For linear case the discreteness of spectrum of corresponding parameter dependent differential operator is obtained. The behavior of solution when the parameter approaches zero and its smoothness with respect to the parameter is established. Moreover, we show the estimate for analytic semigroups in terms of interpolation spaces. This fact can be used to obtain maximal regularity properties for abstract boundary value problems. 相似文献
11.
在自反Banach空间上一个有界线性算子是(B)型良性有界的当且仅当它的共扼算子也是(B)型的。但在非自反Banach空间上这种性质不成立。本文证明在一大类非自反Banach空间上总存在一个(B)型良性有界线性算子,它的共扼算子不是(B)型的。同时也证明了在具有基的Banach空间上,任何P型基序列一定有一个子序弄能够扩张成该空间的一个基。 相似文献
12.
P. Cannarsa G. Da Prato H. Frankowska 《Journal of Mathematical Analysis and Applications》2018,457(2):1173-1187
In a separable Banach space E, we study the invariance of a closed set K under the action of the evolution equation associated with a maximal dissipative linear operator A perturbed by a quasi-dissipative continuous term B. Using the distance to the closed set, we give a general necessary and sufficient condition for the invariance of K. Then, we apply our result to several examples of partial differential equations in Banach and Hilbert spaces. 相似文献
13.
In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results. 相似文献
14.
Derek Kitson 《Journal of Mathematical Analysis and Applications》2011,378(2):680-686
Recent contributions on spaceability have overlooked the applicability of results on operator range subspaces of Banach spaces or Fréchet spaces. Here we consider general results on spaceability of the complement of an operator range, some of which we extend to the complement of a union of countable chains of operator ranges. Applications we give include spaceability of the non-absolutely convergent power series in the disk algebra and of the non-absolutely p-summing operators between certain pairs of Banach spaces. Another application is to ascent and descent of countably generated sets of continuous linear operators, where we establish some closed range properties of sets with finite ascent and descent. 相似文献
15.
一类非线性算子方程解的存在唯一性定理及其应用 总被引:4,自引:1,他引:3
在抽象连续函数空间中,用迭代方法讨论了一类非线性算子方程解的存在唯一性,并将其结果应用于Banach空间中的积分方程. 相似文献
16.
In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces. Various applications are also considered to illustrate our obtained results (existence of solutions to quadratic integral equations with a linear modification of the argument, positive solution of second-order Neumann boundary value problem, and positive definite solutions of a class of nonlinear matrix equations). 相似文献
17.
利用Mnch不动点定理以及一个脉冲积分不等式,研究二阶混合型脉冲积分-微分方程初值问题解的存在性.结果涉及右端项既包含导数又包含积分算子Sx的情形.最后给出了一个应用例子. 相似文献
18.
The traditional Krasnoselskii’s fixed point theorem in Banach spaces does not reproduce the rich and varied forms of operator equations in abstract spaces which are not linear structure. Consequently, its applications to integral equations and differential equations have met many obstacles. The present alternative Krasnoselskii’s fixed point theorem in generalized semilinear Banach spaces overcomes this deficiency and opens up for profitable investigation such as differential systems with uncertainty. An application to the existence of solutions of nonlocal problems for fuzzy implicit fractional differential systems under Caputo generalized Hukuhara differentiability with demonstrated example is given to validate the effectiveness of our theoretical results. 相似文献
19.
I. G. Ismailov 《Computational Mathematics and Modeling》1999,10(1):44-54
We study optimization problems in the presence of connection in the form of operator equations defined in Banach spaces. We
prove necessary conditions for optimality of first and second order, for example generalizing the Pontryagin maximal principle
for these problems. It is not our purpose to state the most general necessary optimality conditions or to compile a list of
all necessary conditions that characterize optimal control in any particular minimization problem. In the present article
we describe schemes for obtaining necessary conditions for optimality on solutions of general operator equations defined in
Banach spaces, and the scheme discussed here does not require that there be no global functional constraints on the controlling
parameters. As an example, in a particular Banach space we prove an optimality condition using the Pontryagin-McShane variation.
Bibliography: 20 titles.
Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 55–67. 相似文献
20.
S. M. Shakhno 《PAMM》2004,4(1):650-651
We apply the method of linear interpolation of Kurchatov to solve nonlinear operator equations in Banach spaces. Using the principle of majorants of L. V. Kantorovich, we study the semilocal convergence of method of Kurchatov. Quadratic order of convergence of this method is determined. A priori and a posteriori estimations of method's error are received. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献