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.     

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.     

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.     

包含Sobolev-Hardy指数的p-Laplace方程的多解

在本文中，我们利用Sobolev-Hardy不等式，局部PS条件和亏格理论，证明了一类带临界Sobolev-Hardy指数的奇异p-Laplace方程存在多解．     

具临界指数椭圆方程-△u=λku+|u|2*-2u+f(x,u)非平凡多解存在性

本文利用山路引理以及P.L.Lions的集中紧性原理,给出了具临界指数2*且涉及任意特征值λk的Dirichlet问题-△u=λku+|u|2*-2u+f(x,u)一对非平凡解的存在性定理,其中次临界扰动项f(x,t)可以是关于变量t的非线性项.     

具临界指数椭圆方程-Δu=λ_κu |u|~(2~*-2)u f(x,u)非平凡多解存在性

本文利用山路引理以及P．L．Lions的集中紧性原理,给出了具临界指数2*且涉及任意特征值λk 的Dirichlet问题-△u=λku |u|2*-2u f(x,u)一对非平凡解的存在性定理,其中次临界扰动项 f(x,t)可以是关于变量t的非线性项．     

具有临界指数的半线性椭圆组弱解的正则性

本文研究具有临界指数的方程组。用ＤｅＧｉｏｒｇｅ估计方法，获得方程组的解的有界性。     

带有临界指数的椭圆型方程的正解的存在性

本文主要采用变分方法来研究一类带有临界指数的椭圆型方程的正解的存在性问题.并且,在Ω领域(有界或无界)中的许多条件下,可以证明其基态解的存在性.     

Ce2Fe16Al化合物在居里温度附近的磁性和磁熵变

研究了具有菱方Th2Zn17型结构的Ce2Fe16Al化合物在居里温度TC附近的磁性和磁熵变.实验结果表明，在居里温度附近样品的磁特性符合二级相变规律，样品的居里温度为2758K.通过磁化强度与磁场和温度关系的测量，计算出临界指数β=044±001，γ=130±001，δ＝383±001，临界指数β，γ，δ基本满足标度率方程γ＝β（δ-1)，但偏离三维Heisenberg模型的理论值.Ce2Fe16Al化合物的磁熵变在居里温度处达到峰值，2T外磁场下的最大磁熵变为195J/kg K. 关键词： Ce2Fe16Al化合物 临界指数 磁熵变     

非经典反应扩散方程在R~3中全局吸引子的存在性

该文证明了带有临界非线性项的非经典反应扩散方程{vt-Δvt-Δu+f(x1,u)=g(x),(x,t)∈R3×R+ u(s,t)|t=0=v0, x∈R3}在H~1(R~3)上的全局吸引子的存在性,推广和改进了文献[15]的结果.