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1.
本文研究如下具阻尼项的Klein-Gordon方程组uu Ut-Δu u-|v|^ρ+2|u|^ρu=0 vu vt-Δv v-|u|^ρ 2|v|c^ρv=0的初边值问题,得到了整体局解的存在唯一性和指数衰减性,给出了当初始能量为正但具有确定上界时及初始能量为负时解的爆破性。  相似文献   

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本文考虑如下非线性发展方程组的初边值问题u″+ Au -△ u′-α| v|ρ+ 2 | u|ρu =0 ,  v″+ Av -△ v′-α| u|ρ+ 2 | v|ρv =0 ,其中 A为 p-Laplace算子 ,α∈ R,ρ>-1均为常数 ,证明了整体解的存在性及渐近性 ,得到了当初始能量为正但有上界时解的爆破性条件  相似文献   

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Sobolev-Hardy不等式与临界双重调和问题   总被引:1,自引:0,他引:1       下载免费PDF全文
该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ,这里Ω包含R^N是包含0的有界光滑区域,u∈H0^2(Ω),μ∈R是参数,0≤s≤2,△^2=△△表示双重拉普拉斯算子,当f(x,u)=u^p,p=2N/N-4时,上述问题就是一个临界双重调和问题,该文运用Sobolev-Hardy不等式和变分方法,得到它的解的存在性的一些结果。  相似文献   

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人口问题中广义三维GINZBURG-LANDAU模型方程   总被引:4,自引:0,他引:4  
本文讨论三维广义Ginzburg-Landau模型方程的初边值问题ut=-a1↓△^4u a2↓△^2u ↓△^2g(u) G(u),σu/σv=0,σ△u/σv=0,u(x,0)=u0(x)解的整体存在性、唯一性、渐近性质和爆破。  相似文献   

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收稿研究带竞争势的非线性Klein-Gordon方程的柯西问题.首先定义了新的稳定集和不稳定集.其次证明了如果初值进入不稳定集,该柯西问题的解在有限时间内爆破;如果初值进入稳定集,该柯西问题的整体解存在.最后运用势井讨论,我们回答了当初值在什么范围时,该柯西问题的整体解存在这个问题.  相似文献   

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In this paper, we study the existence of multiple solutions for the following quasilinear elliptic system:p*(t)|u-2β- △pu1-μ|-2u up1= α1u + β1-2|xp||xt|vβ2||u|u, x∈,|q*β- △qv-μ2 |v|q-2v αv(s)-2|2x|q=|x|sv + β2|uβ1||v2 |-2v, x∈,u(x) = v(x) = 0, x∈ .Multiplicity of solutions for the quasilinear problem is obtained via variational method.  相似文献   

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正则半开集和半同胚空间类   总被引:2,自引:0,他引:2  
设A■X,v为X上的拓扑,用A_v~0、A_v~-、(A_v)_0、(A_v)_-、A’_v分别记A在(X,v)中的内部、闭包、半内部、半闭包和补集。用η_v、ζ_v、ζ_v分别记(X,v)中的半开集族、无处稠密集族和稠密集族。当v=u时,略去上述记号中的足码v。令[u]={v|v为X上的拓扑且  相似文献   

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本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题,定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在.  相似文献   

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对带势的非线性Klein-Gordon方程柯西问题,我们定义了新的对于初值的稳定和不稳定集.我们证明了如果发展进入了不稳定集,解在有限时间内爆破;如果发展进入了稳定集,解整体存在.运用势并讨论,我们回答了当初值为多少时,柯西问题的整体解存在.  相似文献   

10.
三维复Ginzburg-Landau方程的整体解的存在惟一性   总被引:2,自引:0,他引:2  
在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性.  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

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It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

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<正>Aims and Scope Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,is one of the transactions of China Society for Industrial and Applied Mathematics,and is a bimonthly journal.JMRA is dedicated to publishing first-rate original research papers in all areas of mathematics with applications,and making research findings available to a wide scientific world,as JMRE has for many years.In line with the name change,the new scope of Journal of Mathematical Research with Applications will not include the articles on mathematical methodology and mathematical philosophy.Copyright Information  相似文献   

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<正>Erratum to:Science in China Series A:Mathematics,April 2009 Vol.52 No.4:617–630doi:10.1007/s11425-009-0038-2There is a mistake in the proof of[1,Lemma 2.2],which occurs in 4-th line at[1,p.619],  相似文献   

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