MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS

The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.     

STABILITY OF DELAY DIFFERENCE EQUATIONS IN BANACH SPACES

1 IntroductionDiscrete reaction--diffusion type partial difference equations llave recentlybeen introduced by a number of authors as modeIs for the study of spatiotem-poral chaos (see e.g. [2,3j). Stability criteria have also been derived fOr suchequatioIls which invoIve two time-level processes (see e.g. [1l) as well as three-level processes (see e.g. [9]). In this paper, we will study no11linear three--levc1partia1 diffcrence equations in an abstract setting and derive stability criteriafo…     

PERTURBED NONLINEAR EVOLUTION INCLUSIONS IN BANACH SPACES

ＰＥＲＴＵＲＢＥＤＮＯＮＬＩＮＥＡＲＥＶＯＬＵＴＩＯＮＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＸｕｅＸｉｎｇｍｅｉ（薛星美）（Ｄｅｐｔ．ｏｆＭａｔｈ．ａｎｄＭｅｃｈ．，ＳｏｕｔｈｅａｓｔＵｎｉｖ，Ｎａｎｊｉｎｇ２１００１８，Ｃｈｉｎａ．）Ｓｏ...     

THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES

Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B) ? D(C),and let d ∈ L¹(R₊) and 0 ≤β <α ≤2.We characterize the well-posedness of the fractional integro-differential equations D^αu(t)+CD^βu(t)=Bu(t)+∫_-∞^td(t-s)Bu(s)ds+f(t),(0≤t ≤2π) on periodic Lebesgue-Bochner spaces L^p(T;X) and periodic Besov spaces B_p,q^s(T;X).     

A COUPLED SYSTEM OF INTEGRAL EQUATIONS IN REFLEXIVE BANACH SPACES

We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.     

Banach 空间中非线性最佳逼近的广义强唯一性

设X是一致凸空间,G为X中太阳集,R．Smarzewski[1]证明了g∈G对x∈的最佳逼近具有广义强唯一性,本文讨论其逆,在最佳逼近是广义强唯一的条件下,研究了空间的凸性和逼近集的太阳性．     

Banach空间中Volterra非线性积分方程的Carathéodory解

本文在相当弱的条件下研究Ｂａｎａｃｈ空间中Ｖｏｌｔｅｒｒａ非线性积分方程的Ｃａｒａｔｈｅｏｄｏｒｙ解的存在性,证明方法简洁且与现有文献不同．     

MULTIPLE SOLUTIONS OF NONLINEAR FREDHOLM INTEGRAL EQUATIONS IN BANACH SPACES

In this paper, the author uses the topological degree theory to investigate the multiple solutions of nonlinear Fredholm integral equations in Banach spaces. Two new theorems are obtained and two examples are given.     

Banach空间中非线性积分微分方程的迭代解法

通过构造单调迭代序列，研究了Ｂａｎａｃｈ空间中非线性积分微分方程在Ｓｔｕｒｍ边值条件下的最大解与最小解的存在性及其迭代求法。     

MULTIVALUED PERTURBATION TO NONLINEAR DIFFERENTIAL INCLUSIONS WITH MEMORY IN BANACH SPACES

The authors give the existence results to the nonlinear differential inclusion u'(t) ∈ Au(t) F(t,ut), where A is a ganerator of equicontinuous semigroup and F is multivalued.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.     

关于Banach空间中的向量值的Bochner积分型的广义Jensen不等式

李泽民(1990)将R^n中的极值问题的Kuhu-Tucker条件推广到了线性拓扑空间中的向量极值问题．本文作者从另一角度，以锥为工具，把在概率论与鞅论等学科有着广泛应用的R中的著名的Jensen不等式推广到序Banach空间，导出向量值的Bochner积分型的广义Jensen不等式，从而推广了前人的工作．     

Banach空间中一阶非线性脉冲积分-微分方程初值问题

通过引入函数e-λt(其中λ＞0是一给定的常数)和分段利用M(o)nch不动点定理,在非常弱的条件下,建立了Banach空间中一阶非线性脉冲积分-微分方程初值问题整体解的存在性,改进和统一了已有的最近结果.     

Banach空间中非线性脉冲Volterra型积分方程的可解性

本文利用“强极小锥”的概念,获得了Ｂａｎａｃｈ空间中非线性脉冲Ｖｏｌｔｅｒｒａ型积分方程整体解的存在性定理,改进了现有文献中的某些结果．     

A MULTIPLICATION INEQUALITY IN COMPLEX BANACH LATTICE ALGEBRAS

Abstract

We present an alternative order theoretic proof for the fundamental result that |Z₁, Z₂ | ? |Z₁ 1 | Z₂ | with z₂ and z₂ elements of the complexification of an Archimedean uniformly complete Riesz algebra.     

Banach空间非线性脉冲Fredholm型积分方程的耦合拟解及解

本文利用不等式迭代技术和Monch不动点定理,研究了Banach空间非线性脉冲 Fredholm型积分方程耦合拟解及解的存在性,其方法和结果改进并发展了有关文献.     

EIGENVECTORS OF SYSTEM OF HAMMERSTEININTEGRAL EQUATIONS IN BANACH SPACES AND APPLICATIONS

1IntroductionLetEbeaBanachspaceandI=[O,l].ConsiderthesystemofHammersteinintegralequationsinE:wherekiEC[IxI,R'](i=1,2)arenonnegative,fieC[IxExE,E](i=1,2)andyt,YEC[I,E].Inthispaper,weinvestigatetheexistenceofeigenvectorsofsystem(l)bymeansoffixedpointindextheory.WealsogivesomeapplicationstoasystelllofSturm-Liouvilleproblemsofordinarydtherentialequations.Iuwl1atfollows,PdenotesthenormalconeofEwithanormalconstantN(see[1,2l):95u5vimplieslluII5N11vIl,whereoisthezeroelementofE.ExEisaBana…     

Banach空间中的相补问题

本文在Ｂａｎａｃｈ空间中研究了三类相补问题解的存在性。所得结果是［４，５，６，９，１１－１４］中相应结果的深入和发展。