一类带有Neumann边界的奇异拟线性椭圆方程解的存在性

应用变分方法中的极值理论来研究Neumann边界问题{ -div(｜x｜α｜▽u｜p-2▽u)=｜x｜βup(α,β)-1-λ｜x｜γup-1+｜x｜μq-1,u(x)＞0,x∈Ω｜▽u｜p-2?u/?u=0, x∈?Ω其中Ω是RN(N≥3)中具有C2光滑边界的有界区域,0 ∈Ω,n表示(e)Ω的单位外法向向量,且1＜p＜N,α＜0,β＜0,使得p(α,β)(△)p(N+β)/N-p+α＞P,γ＞α-p,P＜q＜p(α,μ).对于参数α,β,γ及μ的不同范围,建立上述方程解的存在性结果.其中对参数不同范围的讨论对解的存在性所起到的至关重要的作用.     

一类具弱阻尼的奇性扰动Boussinesq型方程的位势井方法

采用位势井方法研究一类具弱阻尼的奇性扰动Boussinesq型方程的初边值问题utt-uxx-αux4-βux6 but=σ(u)xx,x∈Ω,t>0,u(0,t)=u(1,t)=uxx(0,t)=uxx(1,t)=ux4(0,t)=ux4(1,t)=0,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,其中uxi=ixui,σ(s)是一个已知的非线性函数,α和β是两个正的实常数,b≥0是任意实数,Ω=(0,1).得到了相应初边值问题整体广义解的存在唯一性.     

一个退化四阶抛物方程弱解的惟一性

证明退化四阶抛物方程ut Δ(Δup-2Δu) λup-2u=0,x∈Ω,t>0,p>2在假定具有自然边界条件u=Δu=0,x∈Ω,t>0,以及初始值条件u(x,0)=u0(x),x∈Ω下,存在弱解惟一性.     

Poisson方程的非线性扰动

考虑Poisson方程的非线性扰动的Dirichlet问题-Δu =g(x) λh(x,u,Du)　　x∈Ω ( 1 )u｜ Ω =0 ( 2 )其中λ∈R ,Ω是Rn 中具有C2 ,α 边界的有界区域 ,n∈N ,α∈ ]0 ,1 [.用截断函数法和Schauder不动点定理得到定理　 设g∈Cα( Ω) ,h∈Cα( Ω×R×Rn) ,则存在δ >0 ,使得当 ｜λ｜<δ时 ,问题 ( 1 ) ,( 2 )在C2 ,α( Ω)中至少有一个解     

β+1

张亚阳  汤军健 《渤海大学学报(自然科学版)》2006,(4)

一类Boussinesq方程整体解的渐近理论

研究如下带阻尼Boussinesq方程Cauchy问题的整体解utt-auttxx-2butxx=-cuxxxx uxx-αu β(up)xx,u(x,0)=ε2(x),　ut(x,0)=ε2ψ(x),其中x∈R1,t>0,a,b,c,α是正常数,β∈R1,ε>0是小参数,p 2是正整数.假设a c-b2>0时,得到了上面问题整体解的适定性及长时间渐近解.     

带非齐次项和Sobolev-Hardy临界指数的奇异椭圆方程的多解

设2*=2(N α)(N-2 β),N≥3,是极限Sobolev指数,ΩRN是RN中的开子集.在f(x)∈Hβ-1满足合适的条件且f(x)≠0下,讨论了一个带非齐次项和Sobolev-Hardy临界指数的含权的椭圆型问题:{-div(|x|β▽u)=|x|αup*-1 εf(x),x∈Ω,u>0,x∈Ω,u=0,x∈Ω,,存在两个解u和-u在H01,,βp(Ω)中,且有u≥0,u-≥0对所有的f(x)≥0.值得注意的是,当f(x)=0时一般不成立.     

一类半线性抛物型方程解性质的注记

在[1]中,研究了发生在燃烧问题和某些非线性扩散问题中的初边值问题:u_t-▽·(D(x)·▽u)=λ(e~(au)-b)(t>0,x∈Ω,)(1)β(()u)/(()v)) u=0(t>0,x∈()Ω)(2)u(0,x)=u_0(x)(x∈Ω),(3)其中Ω是在 R~n 内的一有界区域,()Ω是Ω的边界,λ、β、a、b 是非负常数,0≤6≤1,D 是在()(Ω的闭包)上的正函数,▽是在Ω内的梯度算子,()/(()v)是在()Ω上的外法向导数。     

具临界增长的拟线性退缩椭圆方程Neumann问题正解的多重性

旨在对如下一类临界增长的拟线性退缩椭圆方程的Neumann问题的正解的多重性进行研究.(p)-.(g(uα)uα-2 u)=λ(x)um uq*-1,x∈Ω,g(uα)uα-2 nu ψ(x)u 2α-2u=0,x∈Ω,其中Ω∈RN是N维欧氏空间中的光滑有界区域,u≥0,2≤2α相似文献   

具P（x）—增长条件的2m阶椭圆型方程弱解的存在性

利用广义Orlicz空间L^p(x)和W^m,p(x)(Ω）的基本理论,给出了具有非标准p(x)-增长条件的2m阶椭圆方程{∑1≤│α│≤m(-1)^│α│D^αAα（x,u,Du) g(x,u,Du)=f(x),x∈Ω,D^βu=0,x∈ρΩ,任意│β│≤m-1弱解在存在性。为证明本文的主要结论,还给出了形如W^j m,p(x)(Ω）→W^j,q(x)(Ω）的紧嵌入定理。     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

正~~