A COMPACT EMBEDDING RESULT FOR NONLOCAL SOBOLEV SPACES AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR NONLOCAL SCHRÖDINGER EQUATIONS

For any s∈(0,1),let the nonlocal Sobolev space X^(s)(R^(N))be the linear space of Lebesgue measure functions from R^(N) to R such that any function u in X^(s)(R^(N))belongs to L2(R^(N))and the function(x,y)→(u(x)-u(y)√K(x-y)is in L^(2)(R^(N),R^(N)).First,we show,for a coercive function V(x),the subspace E:={u∈X^s(R^N):f_(R)^N}V(x)u^(2)dx<+∞}of X^(s)(R^(N))is embedded compactly into L^(p)(R^(N))for p\in[2,2_(s)^(*)),where 2_(s)^(*)is the fractional Sobolev critical exponent.In terms of applications,the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation-L_(k)u+V(x)u=f(x,u),x∈R^N are obtained,where-L_(K)is an integro-differential operator and V is coercive at infinity.

BOUNDARY BEHAVIOR OF CAUCHY-TYPE INTEGRALS IN CLIFFORD ANALYSIS

In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF C^n

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bp^σ（B） and p-Carleson measure in the unit ball of C^n. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on Bp（B） spaces by means of Carleson measures for Bp^σ（B）.

POINTWISE MULTIPLICATION OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF ■

This article is devoted to characterizing the boundedness and compactness of multiplication operators from Hardy spaces to weighted Bergman spaces in the unit ball of ■.

Global exponential stability of Cohen-Grossberg neural networks with time-varying delays and impulses

In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.

On Reduced Variational Equations of Coupled Systems

A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symmetry one establishes a structural property for the monodromy matrix of the reduced variational equation,which simplifies the computation of multipliers to a great extent.As an application of the above results,a coupled system of three Poincare oscillators is discussed as well.

PLANE ELASTIC PROBLEMS OF DIFFERENT MEDIA WITH CRACKS ON THE INTERFACE

The equilibrium problem for the infinite elastic plane consisting of two different media with many cracks on the interface is discussed. It is transferred to a boundary value problem for analytic functions and then further reduced to a singular integral equation, the unique solvability and an effective method of solution for which are established. A practical example in applications is illustrated, the solution of which is obtained in closed form.

THE EXISTENCE AND NON-EXISTENCE OF SIGN-CHANGING SOLUTIONS TO BI-HARMONIC EQUATIONS WITH A p-LAPLACIAN

We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^(N),N≥1.By using a special function space with the constraint ∫_(Ω)udx=0,under suitable assumptions on f and g(x,u),we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended.

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF C^n

This article is devoted to studying the decomposition of functions of Qp spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Qp spaces with small scale p, n-1/n〈 p ≤ 1 by means of p-Carleson measure and the Bergman metric on the unit ball of Cn. At the same time, a decomposition theorem for Qp,O spaces is given as well.

The Convergence of Statistically Self Similar Sets and the Upper Bound and Lower Bound of Hausdorff Measure

We constructed a class of self-similar sets and proved the convergence in this paper.Besides these,the upper bound and lower bound of Hausdorff measures of them were given too.

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF C^(n)

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.

A VARIATIONAL PROBLEM ARISING IN REGISTRATION OF DIFFUSION TENSOR IMAGES

The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images.

ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION

This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B.

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.

A Sufficient Condition for k′(z)(k(z)∈H^q,q≥1)to be of H^1

We proved if k(z)∈ Hª(q≥ 1),g(z) is analytic on| ≠ = 1, g(e)+ k(e") q= min g(e")+ h(e)heHq, then k' (z)∈ H' , especially, if q1, then k(z) is an analytic function on the closed unit disk| ≠1.

A Note on the Principal Theorems in the Theory of Functional Analysis

Two theorems are proved. They are with principal significance in functional analysis, for they imply some well known theorems, such as the open mapping theorem, the closed graph theorem and the Banach Steinhaus theorem.

A Theorem of Picard Type for DirichletSeries

An improved version of Mandelbrojt theorems of Picard type for Dirichlet series is given by in.troducing Julia lines.

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

In this paper,we give a survey of some recent progress in terms of verifying Carleson measures;this includes the difference between two definitions of a Carleson measure,the Bergman tree condition,the T1 condition for Besov-Sobolev spaces on a complex ball,vector-valued Carleson measures,Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.