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.     

MORSE THEORY ON BANACH SPACE AND ITS APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS

The author introduces a definition about the nondegeneracy of critical points of a differ-entiable functional defined on a Banach space.Thus the Morse theory is estabished to thesefunctionals on a Banach space with an equivalent differentiable norm.And by use of theMorse inequalities an exension of three critical point theorem due to Krasnoselski,Castro,Lazer and the author is provided.As an application,the multiple solutions of a quasilinearelliptic boundary value problems studied.     

SEMILINEAR RANDOM EQUATIONS WITH A-PROPER OPERATORS IN BANACH SPACE AND THEIR APPLICATION

In this paper the existence of random solutions of operator equations with A-proper Operators is studied. The random analog of deterministic results obtained by Petryshyn in [9] and [10] for such operators is the main theorems. It is then followed by existence reuslts for the Second order differential equation with Newmann boundary value problem.     

LINEARIZED OSCILLATIONS OF DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS

The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation x(t) f(x(t l)) g(x([t-k]))=0 are oblained.     

SOME APPLICATIONS OF BOREL TECHNIQUE IN PARTIAL DIFFERENTIAL EQUATIONS

In this work Borel's technique is applied to analyzing the solvability of partial differetialequations.It is proved that if P is analytic-hypoelliptic,f is C~∞,then the problem for Pu=f with any number of conditions on a fixed point is ill-posed.Besides,some other resultson the flat solution to Laplace equation and wave equation are obtained.     

MULTIPLE SOLUTICNS 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 aro obtained and two examples are given.     

QUASI-INTERPOLATING OPERATORS AND THEIR APPLICATIONS IN HYPERSINGULAR INTEGRALS

1.IntroductionSinceP.ZwartobtainedanexpressionofbivariateB--spline[2],R.--HWangandC.K.Chuihavedevelopedaseriesofresults,especially,thequasi--interpolatingoperatorsofSI(AL.)onuniformtype-2triangulationanditsapproximationproperties[']whichhavewidespreadapplicationsinMechanicsandEngineering.Furthermore,R-HWangandC.K.ChuialsoobtainedthefunctionwithminimumsupportinSI(A:)onnon-uniformtype-2triangulationandthebasisofSI(a:)[#].Inthispaperweintroducesomequasi-interpolatingoperatorsofSa(~Z~)o…     

L_p-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE

The notion of Lp-dichotomy for linear differential equations with possibly unbounded operator is introduced. By help of Banach fixed point theorem sufficient conditions for the existence of bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part are obtained.     

MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.     

THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.     

ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.     

Banach空间随机微分方程的样本最大,最小解的存在性

本文研究了Ｂａｎａｃｈ空间随机微分方程的初值问题的样本最大、最小解的存在性。利用熟知的关于多值映射的可测选择结果，得到了两个此类问题的样本最大、最小解的存在性定理。     

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。     

随机微分—积分方程解的存在唯一性

本文讨论Ｈｉｌｅｒｔ空间中非线性随机微分－积分方程解的存在性,唯一性,在我们所 一组条件下,得到了解的局部存在唯一性的结果。     

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.     

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak*-weak denting point and the weak~*-weak~*denting point of a set.These are the generalizations of the weak~*denting point of a set in a dual Banach space.By use of the weak*-weak denting point,we characterize the very smooth space,the point of weak*-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we al...