PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

AN ITERATIVE ALGORITHM FOR MAXIMAL MONOTONE MULTIVALUED OPERATOR EQUATIONS

A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS FOR FINDING ROOTS OF MAXIMAL MONOTONE OPERATORS

In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.

Some Surjectivity Theorems for Maximal Monotone Operators and Its Application

The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.Especially,some new techniques are used in this paper.

Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

Algorithms of common solutions to quasi variational inclusion and fixed point problems

The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich（Ekonomika i Matematicheskie Metody,1976,12（4）：747-756）,but also extend and replenish the corresponding results obtained by Iiduka and Takahashi（Nonlinear Anal TMA,2005,61（3）：341-350）,Takahashi and Toyoda（J Optim Theory Appl,2003, 118（2）：417-428）,Nadezhkina and Takahashi（J Optim Theory Appl,2006,128（1）：191- 201）,and Zeng and Yao（Taiwan Residents Journal of Mathematics,2006,10（5）：1293-1303）.

RESEARCH ON THE EXISTENCE OF SOLUTION OF EQUATION INVOLVING p-LAPLACIAN OPERATOR

By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta （1978）,the abstract result on the existence of a solution u ∈ L^p （Ω） to nonlinear equations involving p-Laplacian operator △p, where 2N/N＋1〈p〈＋∞ and N （≥ 1 ） denotes the dimension of R^N,is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen＇s previous papers. To obtain the result ,some new techniques are used.

ON A CLASS OF GENERALIZED NONLINEAR IMPLICIT QUASIVARIATIONAL INCLUSIONS

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.

EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.

OPTIMAL CONTROL PROBLEM OF PARABOLIC DIFFERENTIAL EQUATION WITH TWO POINT BOUNDARY CONDITION

This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions tin the time variable). The results here extend those in [3] on optimal control of the heat equations. Moreover, the technique used in this paper is based on some smooth approximations of 'tangent cones' in the sense of Clarke and some maximal monotone operators.

Quadratic minimization for equilibrium problem variational inclusion and fixed point problem

The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

A NEW ALGORITHM FOR MONOTONE INCLUSION PROBLEMS AND FIXED POINTS ON HADAMARD MANIFOLDS WITH APPLICATIONS

In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,.） is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.

MULTIVALUED STOCHASTIC MCKEAN-VLASOV EQUATION

In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.

Iterative Convergence Theorems for Maximal Monotone Operators and Nonexpansive Mappings and Their Applications

In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work.