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...     

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.     

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.     

Banach空间微分方程初值问题

利用半序理论及单调迭代方法研究了Banach空间中非线性微分方程初值问题解的存在惟一性以及解的迭代逼近与误差估计。     

Banach空间泛函微分方程的正解

本文利用锥理论研究Ｂａｎａｃｈ空间泛函微分方程正解的存在性,在紧型条件下获得一个新结果。     

Banach空间中常微分方程的周期解

本文研究Ｂａｎａｃｈ空间中常微分方程的周期解的存在性，在耗散型条件下得到一系列结果。同时，还给出一无穷维微分方程存在周期解的例子。     

Banach空间不连续脉冲微分-积分方程的周期边值问题

本文讨论了Banach空间含间断项的一阶混合型脉冲微分-积分方程的周期边值问题,通过建立一个比较定理,应用不动点定理与上、下解方法证明了最大解、最小解及迭代解的存在性,推广改进了某些文献中的相应结果。     

REMARKS OF DIFFERENTIAL EQUATIONS ON CLOSED SUBSETS IN A BANACH SPACE

1IntroductionTheabstractCauchyproblemsfordifferentialequationsonclosedsetshavebeenstudiedbymanyauthors(see[2],[3]).In[1],H.MonchandG.H.VOnHartonestablishedinequalitiesofmeasuresofnoncolnpactnessforthesequencesofcontinuouslydifferentiablefunctiofls,thed,us…     

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0+ u(t) = f (t, u(t), c D σ 0+ u(t)), t ∈ [0, T ], u(0) = αu(η), u(T ) = βu(η), where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η∈ (0, T ), αη(1 -β) + (1-α)(T βη) = 0 and c D δ 0+ , c D σ 0+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.     

EXISTENCE OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

0 IntroductionRecently, the study of ordinary differential equations in a Banach spacehas been developed extensively by using the strong topology, see [2],13],[4]. Atpresent, however, there is no reference or paper which systematically studiesweak solutions of the Cauchy problem of ordinary differential equation in theweak topology. In references [l],15],[7] and [8], several results of weak solutionsare proved. In this paper, we shall give the other results of weak solutions,some of which are…     

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gteaux differentiable norm. Assume that every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive mappings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, convex optimization problems, and split feasibility problems. Our result extends many recent important results.     

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.     

EFFICIENT AND ACCURATE CHEBYSHEV DUAL-PETROV-GALERKIN METHODS FOR ODD-ORDER DIFFERENTIAL EQUATIONS

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation,third-order equation,third-order KdV equation and fifth-order Kawahara equa-tion are proposed.Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems.Accordingly,both the exact solutions and the approximate solutions are expanded as an infinite and truncated Fourier-like series,respec-tively.Numerical experiments illustrate the effectiveness of the suggested approaches.