共查询到20条相似文献,搜索用时 46 毫秒
1.
许明 《数学年刊A辑(中文版)》2005,(1)
本文在非齐次空间上给出了交换子[b,T](f)=bTf(x)-T(bf)(x)在b(x)是Lipschitz函数时的 Lp(p>1)有界性. 相似文献
2.
本文考虑周期系数的平面Hamilton系统H(x,y,t)=H2(x,y,t)+H4(x,y,t)+d(x,y,t)的平衡解的稳定性。其中H2(x,y,t)=1/2[a(t)x2+y2],H4(x,y,t)=b4(t)x4+b2(t)(xy)2+b0(t)y4以及a(t),b0(t),b2(t),b4(t)是连续的T-周期函数,d(x,y,t)关于时间也是T-周期,在原点附近其阶为(x2+y2)3. 相似文献
3.
Fuzzy本征方程Rx=x全部解的表达式 总被引:1,自引:0,他引:1
本文证明了Fuzzy本征方程Rx=x与Fuzzy本征方程t(R)x=x是等价Fuzzy本征方程.由此,我们得出了一个求任意Fuzzy本征方程全部解的表达式的简便方法. 相似文献
4.
Cantor集的自乘积集的Hausdorff测度的下界 总被引:1,自引:0,他引:1
证明了三分Cantor集C的自乘积集C×C的Hausdorff测度满足 H~(log_3)~4(C×C)≥1.48329。 相似文献
5.
This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equationRoughly speaking, under the assumption that u_ < u+, the solution u(x,t) to Cauchy problem (1) satisfying sup \u(x,t) -uR(x/t)| -0 as t - , where uR(x/t) is the rarefac-tion wave of the non- viscous Burgers equation ut + f(u)x=0 with Riemann initial data 相似文献
6.
<正> 关于奈望利纳(Nevanlinna)氏第二基本不等式曾有引入纪(导)数而作之种种不同的推广,在这些推广式中,极点的密指量每见出现且有特殊作用,因之能否将此量消去是一问题.米约(Milloux)氏及熊庆来教授由不同途径各获得与极点无涉之一不等式此二结果形状互异而各有特点.熊庆来教授指出这两个结果尚可推广到更普遍的境地,我们由此方向探研得如下两个定理,为熊、米二氏者之推广. 相似文献
7.
REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD 下载免费PDF全文
We consider the problem K(x)u xx = u tt , 0 < x < 1, t ≥ 0, with the boundary condition u(0,t) = g(t) ∈ L 2 (R) and u x (0, t ) = 0, where K(x) is continuous and 0 < α≤ K (x) < +∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u(x, ) ∈ H 2 (R) and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem. 相似文献
8.
方程u_(tt)=u_(xxt)+f(u_x)_x初边值问题的差分法 总被引:10,自引:0,他引:10
The finite difference method is considered for the followinginitial-boundary-value problem: arrayllutt=uxxt+f(ux)x, & (x,t) QT, u(x,0) =(x), & x [0,1], ut(x,0) = (x), & x [0,1], u(0,t) =u(1,t) =0, & t [0,T],array. where f(s),(x) and (x) are given functions;QT=[0,1] [0,T]. The convergence of the finite difference schemesis verified by discrete functional analysis methods and prior estimationtechniques. 相似文献
9.
THE BEHAVIOR OF SOLUTIONS IN THE VICINITY OF A BOUNDED SOLUTION TO AUTONOMOUS DIFFERENTIAL EQUATIONS
Lin Guotian 《数学年刊B辑(英文版)》1986,7(2):205-212
By using the exponential dichotomy,this paper investigates the behavior of solutionsin the vicinity of a bounded solution to the autonomous differential systemdx/dt=f(x).(1)Suppose x=u(t)is a nontrivial bounded solution of system(1).By discussing theequivalent equations of system(1)dθ/dt=1 (p,θ)dp/dt=A(θ)p (p,θ)(2)with respect to the moving orthonormal transformationx=u(θ) s(θ)p,the author proves that if linear system corresponding to(2)admits exponential dichotomy,then the given bounded solution x=u(t)should be periodic.The author also discusses thestadility of the obtained periodic solution.Finally,this paper discusses perturbation of thebounded solution of autonomous system(1). 相似文献
10.
本文讨论了实单位球上的平均有界振动M—调和函数的Carleson测度特征,证明了Mobius不变调和函数f(x)属于BMOH或VMOH当且仅当dμ(x)=(1-|x|~2)|f(x)|~2dv(x)是Carleson测度或紧Carleson测度。 相似文献
11.
Hammerstein型非线性积分方程正解的个数 总被引:10,自引:6,他引:4
<正> 本文是作者工作[8]、[9]的继续.在[9]中作者利用Leray-Schauder拓扑度理论研究了多项式型Hammerstein非线性积分方程的固有值,即设 相似文献
12.
YANG XIAOJING 《数学年刊B辑(英文版)》2000,(1)
1.IntroductionInthispaper,wegivesomesufficientconditionsfortheoscillationofallsolutionsofthegeneralizedLi6nardequationi~h(y)~F(x),gi~~g(x).(1.1)Throughoutthispaper,weassumeh(.),F(.),g(.)arecontinuousfunctionsonRandsatisfylocallyLipschitzcondition.MoreoverweassumeF(0)~0;ah(y)>0,y/0;xg(x)>0,x/0;h(y)isstrictlyincreasingandtimh(y)~boo,timG(x)~co,y-boolxl-cowhereG(x)~/".(.)d.,H(y)~l'h(.)d.,icg(u)du,H(y)~['h(u)du,H-'(.),G-'(.)areinversefunctionsofH(.)andG(.).Asolutionof(1.1)issaidtobeoscillato… 相似文献
13.
YANG XIAOJING 《数学年刊B辑(英文版)》2000,21(1)
Some sufficient conditions for oscillation of the generalized Lienard equationsx=h(y)-F(x)x y=-g(x) are given, which generalize the results of[1-7]. 相似文献
14.
<正> 假設級數滿足下面兩個條件,即:(甲)在原點的某一鄰域內,對於h(≠0)的一切值級數收斂; 相似文献
15.
Yan Ziqian 《数学年刊B辑(英文版)》1984,5(1):119-132
In this paper we are concerned with the nonlinear boundary value problem forparabolic system(Lu=f(x,t,u,▽u),x∈Ω,0相似文献
16.
Huang Qichang 《数学年刊B辑(英文版)》1984,5(3):311-318
This paper deal with the existence of periodic solutions of the nonlinear cscillation equation
$$\[\mathop x\limits^{ \cdot \cdot } + f(x)\varphi (x) + \psi (x)\eta (x) = 0\begin{array}{*{20}{c}}
{}&{(3)}
\end{array}\]$$
The author offers a method which can reduce (3) into system
$$\[\mathop x\limits^ \cdot = h(y) - e(y)F(x),\mathop y\limits^ \cdot = - g(x)\begin{array}{*{20}{c}}
{}&{(9)}
\end{array}\]$$
Some sufficient condition for the existence of the limit cycles of (9) are obtained. These results generalize the results in [1,2,3,4,5,6]. 相似文献
17.
DISCUSSION ON THE CONTINUOUS SOLUTIONS OF A FUNCTIONAL EQUATION 总被引:1,自引:0,他引:1
1 IntroductionIn an issue of the American Mathematical Monthly [1] the following problemwas raised:"Determine all homeomorphisms f from [0,1] onto [0,1] that are solutionsof the functional equationf(Zx -- f(x)) = x for all x E [0,IJ.',Ratti and Lin [2] generalized the problem in two different directions. In thispapert we consider the following functional equationf(cr(x) df(x)) = F(x), (1.1)where c < 0,d > 0, c d = 1. We shall give the sufficient conditions ofthe existence, uniqueness a… 相似文献
18.
稳定性理論中第一临界情形的微分方程与微分差分方程的等价性問題 总被引:1,自引:0,他引:1
<正> §1.問題与方法.在[1]中提出了等价性問題,并对于一般n的情形作了系統的研究.本文是处理在第一临界情形下的微分方程与微分差分方程的等价性問題. 問題是研究微分方程組 相似文献
19.
本文研究临界状态下三项Diophantine方程解的问题.运用无穷递降法证明了:设m,n,r是大于1的正整数,当1/m+1/n+1/r=1时,方程xm+yn=zn,min(x,y,z)>1,gcd(x,y)=1无正整数解(x,y,z). 相似文献
20.
Lin Zhengsheng 《数学年刊B辑(英文版)》1984,5(3):363-373
By using the exponential dichotomy and the averaging method,a perturbation theoryis established for the almost periodic solutions of an almost differential system.Suppose that the almost periodic differential system(dx)/(dt)=f(x,t) ε~2g(x,t,ε)(1)has an almost periodic solution x=x_0(t,M)for ε=0,where M=(m_1,…,m_k)is theparameter vector.The author discusses the conditions under which(1)has an almostperiodic solution x=x(t,ε)such that x(t,ε)=x_0(t,M)holds uniformly.The results obtained are quite complete. 相似文献