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1.
本文利用Ekeland的变分原理及山路引理,研究了以下问题在一定条件下的正解的存在性:{-△pu=λuq/|x|s+ur,u>0,x∈Ω(∩)RN,{u(x)=0,x∈(a)Ω,其中△pu=div(| ▽ u |p-2 ▽u),u∈W1,p0(Ω),Ω是RN中的有界区域,且0∈Ω,0<q<p-1,N≥3,0<s<N(p-q-1)p-1 +q+1,p-1<r≤p*-1,p*=Np(N-p)-1,λ>0.此时,s可以大于p,从而推广了p=2时的某些结果.  相似文献   

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胡业新 《应用数学》2005,18(2):286-292
本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数.  相似文献   

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For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.  相似文献   

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讨论非线性Schroedinger方程-△u q(x)u=λu Q(x)│u│^p-1u x∈R^N的解的存在性,其中q(x),Q(x)满足周期性条件,而且Q(x)变号,λ∈R落在-△ q的谱隙中,1<p<N 2/N-2。  相似文献   

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In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space Lp(LogL)a(Ω)(1<p <∞, a ∈ R) is studied. The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω).  相似文献   

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本文讨论了二阶椭圆型方程-△u=f(x,u),x∈Ω的Dirichlet问题u | Ω=0的很弱解u∈W ,r(Ω)(1<r<2)关于区域Ω的连续性及很弱边值问题的很弱解的唯一性.  相似文献   

7.
一类广义的Marcinkiewicz积分算子的有界性   总被引:3,自引:0,他引:3  
研究了下述广义Marcinkiewicz积分算子μΩ,αf(x)=∫∞0|∫|x-y|≤tΩ(x-y)|x-y|n-1f(y)dy|2dtt3+2α12当零次齐次函数Ω∈Hq(Sn-1),q=n-1n-1+α,α≥0,且满足一定的消失性,则对于任意的1相似文献   

8.
讨论非线性 Schrodinger方程-Δu q(x) u =λu Q(x) |u|p- 1u  x∈ RN的解的存在性 .其中 q(x) ,Q(x)满足周期性条件 ,而且 Q(x)变号 ,λ∈R落在 - Δ q的谱隙中 ,1 相似文献   

9.
给出了如下的非线性椭圆方程自由边值问题-Δu=λu+(1+ε)u+p,x∈B Rn,u|Ω=μ,∫Ωnu=-M(1)在C[0,1]中的球对称解的存在性.并得到比上述问题更一般的非线性椭圆方程自由边值问题-Δu=h(u),x∈B Rn,u|Ω=μ,∫Ωun=-M,在C[0,1]中的球对称解的存在性,其中B为Rn中的单位球,p>1,λ>0,μ<0,M>0,ε>0;λ,μ,M,ε均为常数,n为正整数.  相似文献   

10.
廖家锋  李红英  张鹏 《数学学报》2018,61(2):233-242
本文研究了如下非局部临界指数问题{(-a+b∫_Ω|?_u|~2dx)△u=μu~3+λ|x|β~/u~(q-1),x∈Ω,x∈δΩ,其中Ω?R~4是一个有界光滑区域且0∈Ω,a≥0,b,λ,μ0,1q2,0β2.利用变分方法,我们获得了一些存在性与多重性结果.  相似文献   

11.
Cornelia Dru?u 《Topology》2004,43(5):983-1033
We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all -rank one lattices in semisimple groups of -rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion constant.  相似文献   

12.
The present paper outlines some basic principles upon which an outlook in teaching and research in mathematics in educational institutions can be developed. Defining applied mathematics, the author analyses the basic topics of mathematics which permeate throughout the wider fields and diversified aspects of this branch of mathematical science.

For the institutions of learning, a course curriculum has been proposed which will gradually motivate, orient and prepare individuals through the process of learning to understand the methods and techniques, so as to apply them to physical problems. This has been illustrated in the fields of fluid dynamics and aerodynamics through the analysis of complex function theory and differential equations.

Because of the frustrating situations prevailing amongst students and teachers in the institutions of learning in the present day, a critical analysis has been made to identify the respective roles of the academicians and administrators, and with a view to improving the situation, some remedy has been suggested regarding teaching and research in educational institutions.  相似文献   

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A review of recent studies in Hong Kong suggests that possible problems in secondary school algebra may be due to the procedural paradigm orientation in the curriculum and the conventional style of teaching in the classroom which do not provide sufficient opportunities for students to develop conceptual understanding. Based on the works of a number of projects in the West, it is hypothesized that the introduction of technology in lessons which embody a cognitive model in their design and delivery will provide a viable alternative for enhancing algebraic thinking. The key features of the cognitive model are concrete preparation, cognitive conflict, construction, metacognition and bridging, imbedded in a ‘mediation’ style of teaching. These features are exemplified by detailed accounts of classroom episodes from a Hong Kong lesson supported by the use of graphics calculators. Results indicate that while the approach places particular demands on teachers (a tension between a transmission style of teaching and mediating) there is real potential for supporting more dynamic student constructions.  相似文献   

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