Critical Exponent for the Parabolic Equation u_t=Δu~m + h(t)u~p in a Cone

In this paper,we study the initial-boundary value problem of porous medium equation ut = Δum + h(t)up in a cone D =(0,∞) ×Ω,where h(t) ～ tσ.Let ω1 denote the smallest Dirichlet eigenvalue for the Laplace-Beltrami operator on Ω and let l denote the positive root of l 2 +(n 2)l = ω1.We prove that if m p ≤ m + 2(σ+1) n+l + σ(m 1),then the problem has no global nonnegative solutions for any nonnegative u0 unless u0 = 0;if p m + 2(σ+1) n+l + σ(m1),then the problem has global solutions for some u 0 ≥ 0.     

应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠

应用多尺度纠缠重整化算法模拟自旋为1/2的一维量子XYX模型,通过计算局域序参量和度量纠缠的单缠节(one-tangle)、并发纠缠(concurrence)和纠缠比率R,确定系统的基态相图和纠缠相图.发现系统的纠缠相图比基态相图包含更多的物理信息.另外,从局域序参量和能隙与外磁场的标度关系,萃取出与磁化率和关联长度有关的临界指数β和v.     

一类含临界耦合非线性项的奇异椭圆方程组的正解

本文研究了一类含临界指数与耦合非线性项的奇异椭圆方程组. 利用变分方法与极大值原理, 通过证明对应的能量泛函满足局部的 (PS)c 条件, 得到了这类方程组正解的存在性, 推广了单个方程与方程组中的相应结果.     

Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

We consider the following nonlinear problem {-△u=uN＋2/N-2,u〉0 in R^N/Ω,u（x）→0 as｜x｜→＋∞,δu/δn=0 on δΩ,where Ω belong to RN,N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of δΩ. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside （with some symmetries）.     

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.     

具Hardy-Sobolev临界指数的半线性椭圆方程的多解存在性

本文考虑一类具Hardy-Sobolve临界指数的半线性椭圆方程,通过证明局部(P．S．)条件和能量估计,运用伪指标理论得到了这类方程多解的存在性(见文[1-13])．     

有限核多重碎裂中的临界行为与临界指数的提取

利用非对称核物质状态方程可以得到有限核¹¹²Sn的压强－密度等温线, 并对其在坐标和动量空间中的分布进行了模拟, 采用了并合模型对形成的核碎片进行了构造. 通过碎片的关联分析, 寻找出了临界行为的信号, 提取了临界指数.     

无界域上半线性奇异椭圆方程的共振与非共振问题

本文考虑了无界域上一类半线性奇异椭圆方程的加权特征值问题,然后讨论了在非共振与共振情形下这类方程非平凡解的存在性．     

界域上具Hardy临界指数项的半线性椭圆方程的多解存在性

考虑了无界域上一类具Hardy临界指数项的半线性椭圆方程,通过证明局部(P．S．)条件和能量估计,运用伪指标理论得到了这类方程多解的存在性．     

一类临界双调和方程正解的存在性

利用Sobolev-Hardy不等式和山路引理给出了一类带奇异系数和临界指数的双调和椭圆型方程△2u-μu/|x|2=u2*-1u+λur-1/|x|su,u>0,x∈Ω;u=0,x∈■Ω非平凡解的存在性结果.