（K1（x），K2（x））-有限伸张映射

该文首先给出(K1(x),K2(x))一有限伸张映射的定义,然后研究其自我提高的可积性性质.最后利用Caccioppoli型不等式得到可去奇异性结果.     

Nonradial Entire Large Solutions of Semilinear Elliptic Equations

We consider the problem of whether the equation △u = p（x）f（u） on RN, N ≥ 3, has a positive solution for which lim ｜x｜→∞（x） = ∞ where f is locally Lipschitz continuous, positive, and nondecreasing on （0,oo） and satisfies ∫1∞[F （t）]^- 1/2dt = ∞ where F（t） = ∫0^tf（s）ds. The nonnegative function p is assumed to be asymptotically radial in a certain sense. We show that a sufficient condition to ensure such a solution u exists is that p satisfies ∫0∞ r min｜x｜=r P （x） dr = ∞. Conversely, we show that a necessary condition for the solution to exist is that p satisfies ∫0∞r1＋ε min ｜x｜=rp（x）dr =∞ for all ε〉0.     

Multiple solutions for a Schrdinger-Poisson-Slater equation with external Coulomb potential

Consider the following Schrdinger-Poisson-Slater system,(P)u+ω-β|x|u+λφ(x)u=|u|p-1u,x∈R3,-φ=u2,u∈H1(R3),whereω0,λ0 andβ0 are real numbers,p∈(1,2).Forβ=0,it is known that problem(P)has no nontrivial solution ifλ0 suitably large.Whenβ0,-β/|x|is an important potential in physics,which is called external Coulomb potential.In this paper,we find that(P)withβ0 has totally different properties from that ofβ=0.Forβ0,we prove that(P)has a ground state and multiple solutions ifλcp,ω,where cp,ω0 is a constant which can be expressed explicitly viaωand p.     

On a Quasilinear Elliptic Equation with Superlinear Nonlinearities

This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of $\mathbb{R}^{N}$. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.     

Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity

We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.     

One-Dimensional Symmetry and Liouville Type Results for the Fourth Order Allen-Cahn Equation in \RN

In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R~N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.     

Existence and Boundary Behavior of Positive Solutions of Quasi-linear Elliptic Singular Equations with a Gradient term

Existence of positive solutions of a class of quasi-linear elliptic equation with a gradient term is obtained by using super-solution and sub-solution method. In par- ticular, we study the asymptotic behavior of the solution near the boundary up to the second order under various assumptions on the growth of the coefficients of the equa- tion. The results of this paper is new and extend previously known results.     

NONRADIAL POSITIVE SOLUTIONS TO SINGULAR QUASILINEAR ELLIPTIC EQUATIONS IN THE PLANE

This paper investigates 2-dimensional singular,quasilinear elliptic equations and gives some suffcient conditions ensuring the equations have infinitely many positive entire solutions. The super-subsolution method is used to prove the existence of such solutions.     

四阶椭圆方程的一个十六参数能量正交四面体元(英文)

In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation.     

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.     

再议f（x）＝f~（－1）（x）与x＝f（x）是否同解

再议ｆ（ｘ）＝ｆ~（－１）（ｘ）与ｘ＝ｆ（ｘ）是否同解邬坤昌（上海宝山松浦中学）常绪珠（湖北钟祥一中）方程ｆ（ｘ）＝ｆ－１（Ｘ）与方程Ｘ＝ｆ（ｘ）［或Ｘ＝ｆ－１（Ｘ）］是否同解？文［１］以函数ｙ＝１－ｘ的反函数是它自己为反侧，说明了ｆ（ｘ）＝ｆ－１（?..     

SINGULAR POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

The existence and uniqueness of singular solutions decaying like r m(see(1.4)) of the equation u + k i=1 ci|x|li upi = 0,x ∈ Rn(0.1) are obtained,where n ≥ 3,ci > 0,li > 2,i = 1,2,...,k,pi > 1,i = 1,2,...,k and the separation structure of singular solutions decaying like r(n 2) of eq.(0.1) are discussed.moreover,we obtain the explicit critical exponent ps(l)(see(1.9)).     

Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation

Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features.Defning an appropriate metric tensor and designing an efcient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology.In this paper,we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems.We provide an algorithm to generate anisotropic meshes under the given metric tensor.We show that the inverse of the anisotropic difusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects:better discrete algebraic systems,more accurate fnite element solution and superconvergence on the mesh nodes.Various numerical examples demonstrating the efectiveness are presented.     

The Nehari Manifold and Application to a Quasilinear Elliptic Equation with Multiple Hardy-Type Terms

In this paper, by using the Nehari manifold and variational methods, we study the existence and multiplicity of positive solutions for a multi-singular quasilinear elliptic problem with critical growth terms in bounded domains. We prove that the equation has at least two positive solutions when the parameters A belongs to a certain subset of JR.     

The Jacobi Elliptic Function Method for Solving Zakharov Equation

The Zakharov equation to describe the laser plasma interaction process has very important sense, this paper gives the solitary wave solutions for Zakharov equation by using Jacobi elliptic function method.     

Banach空间中—u‘’∈F（t,u（t）,u（t））的解

本文给出了弱序列完备Ｂａｎａｃｈ空间中二阶微分包含的解的存在性定理，推广了「１」中的结果到集值情形，同时由于利用已有的定理「２」，简化了类似「１」宫的证明。     

The Singular Upper Triangle Type Solutions with Spin 1/2 of Quantum Yang-Baxter Equation （I）

In these two papers （I） and （II）, the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper （I）, we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.