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1.
非线性三阶微分方程的四点边值问题   总被引:4,自引:0,他引:4  
用上下解方法研究了三阶非线性微分方程四点边值问题u=f(t,u,u″),a≤t≤b,u(a)=u(a0),u′(a)-δu″(a)=A,u(b)=u(b0),{其中a<a0≤b0<b,δ≥0,A是给定常数.证明了f在适当条件下,上述边值问题有解的充要条件是存在一个下解α和上解β使得α(t)≤β(t),a≤t≤b.  相似文献   

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本文讨论了一类具p-Laplacian算子型奇异边值问题(φp(x'))'+a(t)f(x(t))=0,x(0)-βx(0′)= 0,x(1)+ δx′(1)=0多重正解的存在性,其中φp(x)=|x|p-2x,p>1 通过使用不动点指数定理, 在适当的条件下,建立了这类边值问题存在多重正解的充分条件.这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性.  相似文献   

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一类非线性积分偏微分方程的初值问题   总被引:4,自引:0,他引:4  
讨论初值问题ut-auxxt-p(ux)x-∫t0λ(t-s)q(ux)xds=f(x,t)(-∞<x<+∞)t>0,u|t=0=φ(x),ut|t=0=ψ(x)(-∞<x<+∞){整体经典解的存在性·该问题来源于粘弹性力学·在关于已知函数的一些正则性假设和p′(s)≥c1>0,|q′(s)|≤const,λ(0)<0,λ′(0)<λ2(0)的条件下,通过能量估计,证明了该问题整体经典解的存在性·  相似文献   

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关于Banach空间隐式常微分方程的解的存在性   总被引:3,自引:0,他引:3  
讨论了 Banach 空间中隐式常微分方程 F(t,x,x′) = 0, x(t0 ) = x0 , x′(t0) = y0 的解的存在性,其中, F 的定义域可含无穷远点  相似文献   

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徐中海 《数学研究》1999,32(2):179-183
研 究如下第一边值 问题u t = div(| Du m |p - 2 Dum ) + f (x ,u)u (x ,t) = 0u (x ,0) = u0  0      (x ,t) ∈ Q T = Ω× (0, T)(x ,t) ∈ Ω× (0, T)x ∈ Ω解的极限性质 (t → ∞),推 广了文献[1 ~ 7] 的结果  相似文献   

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关于Fujita型反应扩散方程组的Cauchy问题   总被引:5,自引:1,他引:5  
张凯军  王亮涛 《数学学报》1997,40(5):717-732
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞.  相似文献   

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一类非自治迭代泛函微分方程   总被引:5,自引:0,他引:5  
本文研究了一类非自治迭代泛函微分方程x′(t)=(x2(t)-t2)f(x(x(t)))(其中f∈C(R,R),单调递增,zf(z)>0,z≠0)满足初始条件x(σ)=σ>0,或满足初始条件x(σ)=-σ<0的解的性态、解的存在性及延拓问题.  相似文献   

8.
吴方同 《数学学报》1996,39(6):825-832
设ΩR(n+1),其边界 Ω在x0∈ Ω附近局部为{t=0},且对m阶偏微分算子P(x,t,Dx,Dt)是非特征的.令σm(P)(x,t,ζ,T)=0关于T有m个实根(包括重根)λj(x,t,ζ),(j=1,...,m),且它们是对合组.在P(x,t,Dx,Dt)满足Levi条件下,则其Dirichlet边值问题的解u的C∞奇性在边界的反射锥族中是不变的.  相似文献   

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具有扰动项的泛函微分方程周期边值问题刘辉昭(河北工业大学应用数学系)蒋达清(东北师范大学数学系)利用重合度证明了具有扰动项的混合型泛函微分方程周期边值问题x(t)=b(t,xt)+G(t,xt),0≤t≤T,x(0)=x(T).{解的存在性,这里x(...  相似文献   

10.
设{αk}∞k=-∞为正数缺项序列,满足infkαk+1/dk=α>1,Ω(y′)为Besov空间B0,11(Sn-1)上的函数,其中Sn-1为Rn(n2)上的单位球面.本文证明:若∫Sn-1Ω(y′)dσ(y′)=0,则离散型奇异积分TΩ(f)(x)=∑∞k=-∞∫Sn-1f(x-αky′)Ω(y′)dσ(y′)和相关的极大算子TΩ(f)(x)=supN∑∞k=N∫Sn-1f(x-αky′)Ω(y′)dσ(y′)均在L2(Rn)上有界.上述结果推广了Duoandikoetxea和RubiodeFrancia[1]在L2情形下的一个结果  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   

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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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<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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