Liouville type theorems for a system of integral equations on upper half space

In this paper,we consider the following system of integral equations on upper half space {u(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α) λ1up1(y) + μ1vp2(y) + β1up3(y)vp4(y) dy;v(x) = ∫Rn + (1/|x-y|n-α-1/|-y|n-α)(λ2uq1(y) + μ2vq2(y) + β2uq3(y)vq4(y) dy,where Rn + = {x =(x1,x2,...,xn) ∈ Rn|xn 0}, =(x1,x2,...,xn-1,-xn) is the reflection of the point x about the hyperplane xn= 0,0 α n,λi,μi,βi≥ 0(i = 1,2) are constants,pi≥ 0 and qi≥ 0(i = 1,2,3,4).We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.     

EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s ＜ p, 1 ＜ p ＜ N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ＞ 0,p ≤ r ＜ p* ,p* := Np/N-p is the critical Sobolev exponent, μ＞ 0, 0 ≤ t ＜ p, p ≤ q ＜ p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.     

关于含临界指数的p-平均曲率算子

This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: -div((1 |▽u|~2)(p-2)/2▽u)=λu~(p*-1) μu~(q-1),u＞0,x∈Ω, u=0,x∈■Ω, where u∈W_0~(1,p)(Ω),Ωis a bounded domain in R~N(N＞p＞1)with smooth boundary ■Ω,2＜=p＜=q＜=P~*,P~*=(Np)/(N-p),λ,P＞0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator.     

一类非经典扩散方程在强拓扑空间中的指数吸引子

讨论了非经典反应扩散方程ut-△ut-△u=f(u)+g(x)当非线性项满足临界指数增长时,该方程在强拓扑空间H2(Ω)∩H10(Ω)中的指数吸引子的存在性.特别的,通过证明指数吸引子的存在性,可知文献[7,12,14]中的强拓扑空间中的全局吸引子有有限的分形维数.     

空分流体的临界热力学性质研究

论述了主要空分流体的临界区热力学性质,总结了这些流体目前最为准确的临界参数、临界指数及临界系数实验数据,并与多种模型的计算结果进行了比较.在整合多种流体临界区饱和密度实验数据的基础上,利用幂定律拟合方法得到了统一的临界指数β.该结果与实验数据及重正化群理论计算结果吻合良好.     

A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux

This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources （positive for the first and negative for the second）, where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.     

带临界指数的半线性椭圆型方程的多解性

本文讨论了半线性椭圆方程 -刀u+且u=±a(x)|u|(?),x正赝;u=0,x正日口非平凡解的存在性.其中赝cR~n(n≥4)是有界光滑区域,丸为常数.我们在a(x)比较弱的假设下得到上述方程解的存在性结果.     

Brezis－Kato定理的一个推广

利用ＤｅＧｉｏｒｇｅ估计获得了临界指数方程的有界性结果，改进了Ｈ．Ｂｒｅｚｉｓ和Ｔ．Ｋａｔｏ相应的工作。     

On critical exponents for semilinear heat equations with nonlinear boundary conditions

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一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.