PROPERTIES OF TENSOR COMPLEMENTARITY PROBLEM AND SOME CLASSES OF STRUCTURED TENSORS

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor ,4 such that the tensor complementarity problem （q, A）： finding an x ∈R^n such that x ≥ 0, q＋Axm-1 ≥ 0, and xT（q＋Ax^m-1） = 0, has a solution for each vector q ∈R^n. Several subclasses of Q-tensors are given： F-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal entries are positive, and so the equivalence of Q-tensor, R-tensors, strictly semi-positive tensors was showed if they are nonnegative tensors. We also show that a tensor is an R0-tensor if and only if the tensor complementarity problem （0, A） has no non-zero vector solution, and a tensor is a R-tensor if and only if it is an R0-tensor and the tensor complementarity problem （e,A） has no non-zero vector solution, where e = （1, 1…. , 1）T

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.

FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRA-LEVIN EQUATIONS

In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.

EXISTENCE OF ALMOST PERIODIC SOLUTIONS TO SOME SEMI-LINEAR STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.

EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.

DIAGNOSABILITY OF CAYLEY GRAPH NETWORKS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS MODEL

Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay（Tn,Sn） generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system.In this paper,it is proved that diagnosability of Cay（Tn,Sn） is n-1 under the comparison diagnosis model for n ≥ 4.

EXISTENCE OF PERIODIC SOLUTION FOR A KIND OF(m, n)-ORDER GENERALIZED NEUTRAL DIFFERENTIAL EQUATION

In this paper, we consider the following high-order p-Laplacian generalized neutral differential equation with variable parameter(φp(x(t)-c(t)x(t-σ))(n))(m)+ g(t, x(t), x(t-τ(t)), x′(t), ···, x(m)(t)) = e(t).By the coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solutions are established.

THE EULER EQUATION AND ONSAGER CONJECTURE

In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.

PERMANENCE OF PERIODIC BEDDINGTONDEANGELIS PREDATOR-PREY SYSTEM IN A TWO-PATCH ENVIRONMENT WITH DELAY

In this paper, we study a two-species periodic Beddington-De Angelis predator-prey model with delay in a two-patch environment, in which the prey species can disperse between two patches, but the predator species cannot disperse. On the basis of the comparison theorem of differential equations, we establish sufficient conditions for the permanence and extinction of the system.

L^p SOLUTIONS TO BSDES WITH MONOTONIC AND UNIFORMLY CONTINUOUS GENERATORS

In this paper, we deal with Lp(p 】 1) solutions to one dimensional backward stochastic differential equations(BSDEs) with discontinuous(left or right continuous)generators. We obtain an existence theorem of Lpsolutions to BSDEs whose generators are discontinuous, monotonic in y and uniformly continuous in z.

PERIODIC SOLUTIONS FOR A CLASS OF DEGENERATE NEUTRAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point method, discusses the problem of periodic solution for a class of degenerate neutral periodic system with delay, and obtains some sufficient conditions for the existence and uniqueness of periodic solution of the system, the result extends and improves some results of paper [1-2].

STATIONARY OSCILLATION OF INTERVAL SYSTEM

In this paper, the methods of decomposition of large-scale system and Liapunov function are used in studying the existence of stationary oscillation of periodic interval system, some new results are obtained.

EXISTENCE OF PERIODIC SOLUTION TO GENERALIZED NEUTRAL LINARD DIFFERENTIAL EQUATION

In this paper, we consider a generalized neutral Li′enard differential equation. By applications of coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solution is established.

THE STRUCTURE OF EIGENVALUE REGIONS FOR A TWO-DELAY DIFFERENTIAL SYSTEM WITH A TWIN-PARAMETER

This paper is concerned with positive solutions and the structure of eigenvalue regions for a two-delay singular differential system with a twin-parameter.

ASYMPTOTIC BEHAVIOR OF WAVE EQUATION OF KIRCHHOFF TYPE WITH STRONG DAMPING

The paper deals with the strongly damped nonlinear wave equation of Kirchhoff type. The existence of a global attractor is proven by using the de- composition, and moreover, the structure of the global attractor is established. Our results improve the previous results.

ON NONOSCILLATORY SOLUTIONS OF HIGHER ORDER NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS

In this paper necessary and sufficient conditions for the existence of nonoscillatory solutions of a class of higher order nonlinear functional differential systems are obtained.

A LOCAL ATTRACTOR FOR A NONLINEAR WAVE EQUATION ARISING IN ELASTIC WAVEGUIDE MODEL

This paper studies the asymptotic behavior of solutions to the initial boundary value problem for a nonlinear wave equation arising in an elastic waveguide model. It proves that under rather mild conditions on g the related solution semigroup possesses a local attractor.

EFFECTIVE STABILITY FOR NEARLY INTEGRABLE MAPPINGS WITH INTERSECTION PROPERTY

We consider a nearly integrable mapping with a fixed twist frequency. Under the intersection property and Diophantine condition we prove that the mapping possesses effective stability. In particular, the mapping considered may have different dimensions of action-angle variables in our case.