Finite difference schemes of the nonlinear pseudo-parabolic system

ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＰＳＥＵＤＯ－ＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＤＵＭＩＮＧＳＨＥＮＧ（杜明笙）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔ...     

广义同步化流形的Holder连续性

证明了两个不同的混沌系统线性耦合时能实现广义同步化,在一定条件下广义同步化流形是Holder连续的.采用的思想是Temam的无穷维动力系统的惯性流形理论的改进.在线性耦合下两个混沌系统具有吸收集和吸引子的基础上,通过定义在一个函数类上的映射满足Schauder不动点定理,从而得到广义同步化流形,该广义同步化流形具有不变性.又证明了存在分数维的指数吸引子,指数吸引子与广义同步流形的交集具有指数吸引性.数值仿真证实了理论的正确性.在驱动系统和响应系统外引入辅助系统,辅助系统与响应系统的完全同步化表明了驱动系统和响应系统的广义同步化.     

Well-posedness of a general class of elliptic mixed hemivariational–variational inequalities

In this paper, well-posedness of a general class of elliptic mixed hemivariational–variational inequalities is studied. This general class includes several classes of the previously studied elliptic mixed hemivariational–variational inequalities as special cases. Moreover, our approach of the well-posedness analysis is easily accessible, unlike those in the published papers on elliptic mixed hemivariational–variational inequalities so far. First, prior theoretical results are recalled for a class of elliptic mixed hemivariational–variational inequalities featured by the presence of a potential operator. Then the well-posedness results are extended through a Banach fixed-point argument to the same class of inequalities without the potential operator assumption. The well-posedness results are further extended to a more general class of elliptic mixed hemivariational–variational inequalities through another application of the Banach fixed-point argument. The theoretical results are illustrated in the study of a contact problem. For comparison, the contact problem is studied both as an elliptic mixed hemivariational–variational inequality and as an elliptic variational–hemivariational inequality.     

Asymptotic behavior of optimal solutions to control problems for systems described by differential inclusions corresponding to partial differential equations

In the paper, we consider differential inclusions related to PDEs of parabolic type and some control problems with integral cost functionals associated to them. Given a sequence of such problems, we investigate first the asymptotic behavior of solution sets (mild solutions or more precisely selection-trajectory pairs) for differential inclusions, and we get some semicontinuity or continuity results (Kuratowski convergence of solution sets). Then, we prove the -convergence of cost functionals, related to the above Kuratowski convergence of solution sets. Finally, applying the Buttazzo-Dal Maso abstract scheme, based on the sequential -convergence, we obtain results concerning the asymptotic behavior (hence, also stability results) for optimal solutions to control problems as well as the convergence of minimal values.The authors would like to thank Professors G. Dal Maso and S. Spagnolo for helpful conversations.This work was done when the first author was visiting ICTP and ISAS in Trieste in 1990/91.     

Banach空间中广义的Sturm-Liouville m点边界值问题的正解(英文)

By applying the fixed-point theorem of strict-set-contraction,this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach spaces.     

带p-laplace算子的两点边值问题三个正解的存在性

利用一个不动点定理,研究一类具有p-laplace算子的二阶微分方程的两点边值问题(φp(x′(t)))′+q(t)f(t,x(t),x′(t))=0,x(0)-B(x′(0))=0,x(1)+B(x′(1))=0.给出了三个正解存在的充分条件.推广并丰富了以往文献的一些结论.     

POSITIVE PERIODIC SOLUTION TO SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH MIXED DELAY

We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii's fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.     

On inertial proximal algorithm for split variational inclusion problems

ABSTRACT

In this paper, a hybrid proximal algorithm with inertial effect is introduced to solve a split variational inclusion problem in real Hilbert spaces. Under mild conditions on the parameters, we establish weak convergence results for the proposed algorithm. Unlike the earlier iterative methods, we do not impose any conditions on the sequence generated by the proposed algorithm. Also, we extend our results to find a common solution of a split variational inclusion problem and a fixed-point problem. Finally, some numerical examples are given to discuss the convergence and superiority of the proposed iterative methods.