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1.
研究了非线性悬臂梁方程u(4)(t)=f(t,u(t),u′(t)),0相似文献   

2.
Glimm方法对于燃烧模型组的收敛性   总被引:1,自引:0,他引:1  
本文对于反应速率无穷的燃烧模型组的初值问题 (u qz)/t f(u)/X=0, s(x,t)=0,sup_(0≤τ≤t) u(x,τ)>0,t≥0,-∞0,f~(11)(u)≥δ>0(u≥0),常数q>0以及当u_0(x)>0时s_0(x)=0。  相似文献   

3.
In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian(Φp(u000))0(t)+a(t)f(t, u(t?τ), u0(t))=0, 0〈t〈1;u000 (0)=u00 (0)=0, u0 (1)=αu0 (η);u(t)=0, ?τ ≤t≤0. By using Schauder fixed-point theorem, some su?cient conditions are obtained which guar-antee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.  相似文献   

4.
吴红萍 《数学研究》2007,40(3):305-308
利用锥上的不动点定理证明了二阶Nuemann特征值问题-u″+Mu=λa(t)f(u(t))m0≤t≤1 u′(0)=u′(1)=0是的正解存在性结果.  相似文献   

5.
杨和 《大学数学》2011,27(5):33-38
研究了四阶两参数常微分方程周期边值问题{u(4)(t)-βu″(t)+αu(t)=f(t,u(τ(t))),t∈[0,1],u(i)(0)=u(i)(1),i=1,2,3正解的存在性、多重性和不存在性.在非线性项f(t,u)变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问...  相似文献   

6.
一维p-Laplacian奇异Sturm-Liouville边值问题的正解   总被引:18,自引:0,他引:18  
本文在条件 0 ≤ f+ 0 <p(M1) ,p(m1) 1 ,f+ 0 =limu→ 0f(u)p(u) ,f-∞ =limu→∞f(u)p(u) ,f-0 =limu→ 0f(u)p(u) ,f+ ∞ =limu→∞f(u)p(u) ,g在区间 [0 ,1 ]的端点可以具有奇性 .  相似文献   

7.
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0.  相似文献   

8.
研究了下面分数阶微分方程边值问题正解的存在性和唯一性D0+αu(t)=f(t,u(t)),00+α是标准的Riemann-Liouville微分,f:[0,1]×[0,∞)→[0,∞)连续。首先应用压缩映像原理得到解的唯一性,其次应用不动点指数得到正解的存在性,证明中借助了特征值理论。  相似文献   

9.
几类半线性椭圆共振问题   总被引:1,自引:0,他引:1  
设Ω∪→R^n是一个有界正则区域,{λk}是-△在H0(Ω)上的一列特征值。假定对某个给定的k,λk是单重的,φ为其相应的特征函数,∫φ^2=1,固定h∈H^-1使∫hφ=0。对于方程(P1){-△u-λu g(x,u)=tφ h,u=0。σΩ本文利用连通技巧和闭联集理论,推广了文[1]、[3]、[4]中的一些结果。我们获得定理1 假设g:R^*→R满足(g1)g是具有周期原函数的连续周期函数,λk(k≥)简单。如果对任意s ∈R,有(H′4{λk-1≤λ g′(s)≤λk 1k>1。const≤λ g′(s)≤λ2。则任意h∈H^1,E←τ1,τ2∈R。τ1≤0≤τ2使(i)(P1)有解当且仅当t∈[τ1,τ2]。(ii)如果t∈[τ1,τ2]-{0},则(P1)至少有两个不同的解。定理2 假设(H′4)成立,λk简单,g满足(H2)任意s,g按x在Ω上可测;g∈C^1对a.e.x∈Ω。(H5)g有界limsg(x,s)=μ>0。|s|→∞则任意h∈H′0, E←τ1,τ2∈R,τ1<0<τ2使(i)(P1)有解当且仅当t∈[τ1,τ2]。(ii)若t∈[τ1,τ2]-{0},则(Pt)至少有两个不同的解。定理3 [3,prop.2.4]中的条件q<v(-△-λkI)换成q≤v(-△-λkI)结论仍然成立。  相似文献   

10.
利用Leggett—Williams不动点定理,研究了二阶时滞微分方程边值问题 {y"(t)+f(t,y(t-τ))=0,0〈t〈2π; y(t)=0,-τ≤t≤0; y(0)=y(2π) 正解的存在性.其中0〈r〈π/2为一常数.我们先建立了该问题至少存在两个正解的充分条件.接着给出其至少存在三个正解的存在定理.  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   

13.
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   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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