一类非线性四阶椭圆型方程的极值原理及其特征值问题

主要应用 Hopf极值原理 ,对一类非线性四阶椭圆型方程Δ2 u +h( x,u,Δu) =0进行研究 ,得到解的泛函的极值原理 .类似的文章结果也有许多 ,其方法均为构造适当的“P-泛函”,但是以前的结果都对方程有较强的要求限制 .本文通过构造新的泛函 ,减弱了要求限制 .同时对方程Δ2 u +λh( x,u,Δu) =0的特征值给出了估计 .     

一类离散m点边值问题正解的存在性和多重性

运用锥拉伸与锥压缩的Krasnosel’skii不动点定理,讨论了一类离散m点边值问题Δ2u(k)+λa(k)f(u(k))=0,k∈N,Δu(0)=∑m-2i=1biΔu(li),u(T+2)=∑m-2i=1aiu(li).在不要求极限li mu→0f(u)u,lui→m∞f(uu)存在的情形下,得到了其正解的存在性、非存在性和多重性的充分条件,推广了文[1]的相应结果.     

类渐近线性p＆q—Laplace方程弱解的全局衰减性

该文研究椭圆型方程{-Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x,u),x∈RN,u∈ W1,p(RN)∩W1,q(RN)弱解在全空间RN上的衰减性,其中m,n≥0,N≥3,1相似文献   

临界非齐次双调和方程的多解存在性

该文讨论了下列边值问题Δ2 u =λu |u|p- 1u μf (x) ,x∈Ω ,μ >0 ;u| Ω =0 , u n Ω =0 .的多解存在性和非存在性 .其中 :Ω RN是有界光滑区域 ,N≥ 5,λ∈ R1,P =N 4N - 4,f(x)是Ω中的非负不恒为零的连续函数 ,Δ2 =ΔΔ表示 N维双调和算子 .     

Δ2u=λu+(uN+4－N-4)+μf(x)的多解存在性

讨论了非齐次双调和方程边值问题{Δ2u=(入u)+(uN+4－N-4)+(uf)(x),x∈Ω,u|(аΩ)=Δu|(аΩ)=0,的两个正解的存在性和非存在性.这里Ω是RN内有界光滑区域,N>4,λ∈R1,μ≥0,f(x)是非负连续函数.     

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

We investigate the bi-harmonic problem ■ where Δ² u=Δ（Δu）,Δ_pu=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.     

抛物型薛定谔方程的最优正则性估计(英文)

本文通过特征化抛物型薛定谔算子t-Δ+V的域,探讨了抛物型薛定谔方程u/t-Δu+Vu=f在Orlicz空间中的最优正则性估计,并且对空间的维数没有限制.     

一类无穷阶退化抛物方程解的存在性

设X=(X_1,...,X_m)是一组无穷阶退化向量场,Δ_X=Σ_(j=1)~m X_j~*X_j,其中X_j~*是X_j的形式自伴算子.运用不动点理论得到抛物方程u_t=Δ_Xu+u log|u|解的存在性.     

一类离散型Bellman-Bihari不等式及其应用

本文建立了一类新的更为广泛的非线性离散不等式.所得结果改进并推广了文中的有关结果.并利用所得结果考虑了差分方程Δ²u(n)+f(n,u(n),Δu(n))=0解的渐进性质,其中(n,u,ν)∈N×R×R,N=1,2,….     

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.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.