SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY

In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa, G. Gundersen and J.K. Langley, Li Chun-hong.

The Growth of the Zero Dirichlet Series in Right Half Plane

飞机被学习的在一半的零目和他们的生长上的二条定理的 Dirichlet 系列在这份报纸被获得。

ESTIMATES FOR THE HYPER-ORDER OF SOLUTIONS OF CERTAIN LINEAR DIFFERENTIAL EQUATIONS

In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.

THE MONOTONICITY OF CONVERGENCE RATE FOR MGS METHODS

In this paper we prove that the convergence rate of the modified Gauss-Seidel method is a monotonic function for some precondition parameters.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.

ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES

In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-function for the first time.

ON THE INVERSE IMAGE SET OF RATIONAL FUNCTIONS

This article studies the inverse image of rational functions. Several theorems are obtained on the Julia set expressed by the inverse image, and a mistake is pointed out in H.Brolin＇ theorem incidentally.

BLOCK H-MATRICES AND SPECTRUM OF BLOCK MATRICES

The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.

LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.

THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS

In this article, the authors show the existence of global solution of two-dimensional viscous Camassa-Holm (Navier-Stokes-alpha) (NS-α) equations. The authors also prove that the solution of the NS-α equations converges to the solution of the 2D NS equations in the inviscid limit and give the convergence rate of the difference of the solution.

THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS

In this article, the generalized Roper-Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in C^n are extended to Hilbert spaces or Banach spaces.

On the Extension Operator in Banach Spaces

In [1], Roper and Suffridge introduced an extension operator. This operator is defined for normalized locally univalent function f on the unit disc U = {z ∈ C: |z| ＜ 1} in C by Фn(f)(z)=(f(z1),√f'(z1)z0),where z = (z1,z0) belongs to the unit ball Bn in Cn, z1 ∈ U, z0 = (z2,…,zn) ∈ Cn-1, and we choose the branch of the square root such that √f'(0) = 1.

PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

We study the partial regularity of weak solutions to the 2-dimensional Landau- Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.

Normal family of quasimeromorphic mappings

The more general quasimeromorphic mappings are studied with the geometric method. The necessary and sufficient conditions for the normality of the family of quasimeromorphic mappings are discussed. We proved two inequalities on the covering surface and obtained some normal criteria on quasimeromorphic mappings with them. Obviously, these criteria hold for meromorphic functions.

Kamenev-type Oscillation Criteria for Semilinear Elliptic Differential Equations

Oscillation criteria for semilinear elliptic differential equations are obtained. The results are extensions of integral averaging technique of Kamenev. General means are employed to establish our results.

Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa＇s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .

A Note on the Product Borel Probability Measure

在这份报纸，是在一些紧缩的公制的空格的产品空间的产品 Borel 概率措施的一项措施的一个必要、足够的条件被给。