共查询到20条相似文献,搜索用时 31 毫秒
1.
<正> 导言伯恩斯坦曾经证明:设 F(x)是偶的整函数,其泰勒系数不是负数,并且它的性(род,genus)大于零.如果 f(x)在(—∞,∞)上连续,并且适合 相似文献
2.
高继 《应用泛函分析学报》2000,2(3):247-263
假设S(X)是Banach空间X的单位球面,作引进了四个新的几何参数:Jε(X)=sup{βε(x),x∈S(X)},jε(X)=inf{βε(x),x∈S(X)},Gε(X)=sup{αε(x),x∈S(X)},gε(X)=inf{αε(x),x∈S(S)},其中≤ε≤1,βε(x)=sup{min{‖x εy‖,‖x-εy‖,y∈S(X)}},αε(x)=inf{max{‖x εy‖,‖x-εy‖,y∈S(X)}},讨论了这些参数的性质,本主要结果是:如果主要结果是:如果有一个ε,0≤ε≤1,使得Jε(X)<1 ε/2或gε(X)>1 ε/3,那末X有一至正规结构。 相似文献
3.
Xie Xingwu 《大学数学》1998,(4)
本文对[n/n]Padé逼近进行探讨,证明了Pn(x)/Qn(x)是函数f(x)在x=0处的[n/n]Padé逼近,而Qn(x)=Pn(-x)的充要条件是f(x)f(-x)=1,从而使这一类函数的[n/n]Padé逼近计算量减少一半. 相似文献
4.
Alexei V. Bourd 《Journal of Difference Equations and Applications》2013,19(2):211-225
We investigate the asymptotic behavior of solutions of the system x ( n +1)=[ A + B ( n ) V ( n )+ R ( n )] x ( n ), n S n 0 , where A is an invertible m 2 m matrix with real eigenvalues, B ( n )= ~ j =1 r B j e i u j n , u j are real and u j p ~ (1+2 M ) for any M ] Z , B j are constant m 2 m matrices, the matrix V ( n ) satisfies V ( n ) M 0 as n M X , ~ n =0 X Á V ( n +1) m V ( n ) Á < X , ~ n =0 X Á V ( n ) Á 2 < X , and ~ n =0 X Á R ( n ) Á < X . If AV ( n )= V ( n ) A , then we show that the original system is asymptotically equivalent to a system x ( n +1)=[ A + B 0 V ( n )+ R 1 ( n )] x ( n ), where B 0 is a constant matrix and ~ n =0 X Á R 1 ( n ) Á < X . From this, it is possible to deduce the asymptotic behavior of solutions as n M X . We illustrate our method by investigating the asymptotic behavior of solutions of x 1 ( n +2) m 2(cos f 1 ) x 1 ( n +1)+ x 1 ( n )+ a sin n f n g x 2 ( n )=0 x 2 ( n +2) m 2(cos f 2 ) x 2 ( n +1)+ x 2 ( n )+ b sin n f n g x 1 ( n )=0 , where 0< f 1 , f 2 < ~ , 1/2< g h 1, f 1 p f 2 , and 0< f <2 ~ . 相似文献
5.
Toshihiko Hoshiro 《偏微分方程通讯》2013,38(5-6):905-922
The hypoelliticity is discussed for operators of the form P=D2 x+a(x)D2 y+b(x)Dywhere a (x) and b (x) are real–valued C∞ functions satisfying a(0)=0 and a(x) >0 for x≠0.We seek the conditions for P to be hypoelliptic, especially in the case where both a (x) and b(x) vanish to infinite order on x=0. 相似文献
6.
指数分布族参数的渐近最优与可容许的经验Bayes估计 总被引:3,自引:1,他引:2
在平方损失下 ,构造了指数族 { f(x|λ) =λe-λx,λ >0 ,x >0 }的参数λ的渐近最优与可容许的经验Bayes估计 ,即δn=(n +u + 1n1φ(n) + 1) β1+ βX,其中X1,X2 ,…Xn(历史样本 )和X(当前样本 )独立同分布于 f(x) ,Sn= ni=11n(1+ βXi) ,φ(n) =1n(Sn+ 1n(1+ βX) +v- 1) ,u >0 ,v >0 ,β >0 (已知 )为任意的实数 ,并证明了该估计的收敛速度为O(n- 1)。 相似文献
7.
Debra L. Etheridge Jesu´s Rodriguez 《Journal of Difference Equations and Applications》2013,19(5):447-466
In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions. 相似文献
8.
研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1
相似文献
9.
研究三阶奇异边值问题-x=f(t,x,x,′x)″,t∈(0,1),x(0)=x(′0)=x(′1)=0,其中f:(0,1)×(0,∞)×R×R→R连续,f在x=0,t=0与t=1处具有奇性.通过运用上下解方法和单调逼近理论,得到了该问题新的正解的存在性结果. 相似文献
10.
考虑带p-Laplacian算子的四阶四点边值问题(φp(x″(t)))″=f(t,x(t),x″(t)),t∈[0,1],x(0)-αx′(0)=0,x(1)+βx′(1)=0,φp(x″(ξ))-γ(φp(x″(ξ)))′=0,φp(x″(η))+δ(φp(x″(η)))′=0,其中φp(s)=s p-2s,p>1;0<ξ,η<1;f∈C([0,1]×R2,R).通过建立上下解方法得到迭代解的存在性. 相似文献
11.
设n≥2,Ω为R~n中单位球面S~(n-1)上的可积函数且Ω在S~(n-1)上的平均值为零,即∫_S~(n1)~Ω(x)dσ(x)=0.其中dσ为S~(n-1)上的体积元.定义奇异积分算子T_0,和相应的极大算子T~*,其中h∈L~∞(R~+).关于算子T和T~*已有许多研究([1]-[6]等).在1986年,Namazi利用Fourier变换的Hausdorff-Young不等式证明了 相似文献
12.
V. E. Katznel'son 《Journal of Mathematical Sciences》1981,16(3):1095-1101
Letf be an entire function (in Cn) of exponential type for whichf(x)=0(?(x)) on the real subspace \(\mathbb{R}^w (\phi \geqslant 1,{\mathbf{ }}\mathop {\lim }\limits_{\left| x \right| \to \infty } \phi (x) = \infty )\) and ?δ>0?Cδ>0 $$\left| {f(z)} \right| \leqslant C_\delta \exp \left\{ {h_s (y) + S\left| z \right|} \right\},z = x + iy$$ where h, (x)=sup〈3, x〉, S being a convex set in ?n. Then for any ?, ?>0, the functionf can be approximated with any degree of accuracy in the form p→ \(\mathop {\sup }\limits_{x \in \mathbb{R}^w } \frac{{\left| {P(x)} \right|}}{{\varphi (x)}}\) by linear combinations of functions x→expi〈λx〉 with frequenciesX belonging to an ?-neighborhood of the set S. 相似文献
13.
Dong Yujun 《Proceedings of the American Mathematical Society》1998,126(1):145-152
In this paper, based on of the concept , which is a generalized form of the first resonant point to the Picard problem , , we study the solvability of second-order Sturm-Liouville boundary value problems at resonance , , , and improve the previous results about problems derived by Chaitan P. Gupta, R.Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.
14.
本文研究边值问题:εy"=f(x,y,y',ε,μ)(μ0(ε,μ)y(x,ε,μ)|(x=1-μ)=φ1(ε,μ)其中ε,μ是两个正的小参数 在fy’≤-k<0和其他适当的限制下,存在一个解且满足其中y0,0(x)是退化问题 f(x,y,y',0,0)=0(01(0,0)的解,而yi-j,j(x)(j=0,1,…,i;i=1,2,…m)能够从某些线性方程逐次求得. 相似文献
15.
J. R. Cannon 《Annali di Matematica Pura ed Applicata》1964,66(1):155-165
Summary Let u(x, t) satisfy the heat equation in 0<x<1, 0<t≤T. Let u(x, 0)=0 for 0<x<1 and let |u(0, t)|<ε, | ux(0, t) |<ε, and | u(1, t) |<M for 0≤t≤T. Then,
, where M1 and β(x) are given explicitly by simple formulas. The application of the a priori bound to obtain error estimates for a numerical
solution of the Cauchy problem for the heat equation with u(x, 0)=h(x), u(0, t)=f(t), and ux(0, t)=g(t) is discussed.
Work performed under the auspices of the U. S. Atomic Energy Commission. 相似文献
16.
Wang Cunqi 《数学年刊B辑(英文版)》1987,8(4):404-409
The development of the inverse scattering transform(I.S.T)has made it possible tosolve certain physically significant nonlinear evolution equations with periodic boundaryconditions.Date and Tanaka have considered kdv equation;Ma and Ablowitz havediscussed the cubic Schrodinger equation.In this paper,following closely the analysis in[2,3]the author considers Harry-Dym eqution(q~2)_t=-2r_(xxx)(Ⅰ)where q(x,t)is periodic in x with period π for all time q(x,t)=q(x π,t),q(x,t)=r~(-1)(x,t)>0 相似文献
17.
本文研究一类二阶脉冲微分方程:■的正解存在性.其中,0<η<1,0<α<1,f:[0,1]×[0,∞)×R→[0,∞),I_i:[0,∞)×R→R,J_i:[0,∞)×R→R,(i=1,2,…,k)均为连续函数.本文所用方法是文献[5]推广的Krasnoselskii不动点定理,此定理为解决依赖于一阶导数的边值问题提供了理论依据.基于此定理,获得了问题正解存在性定理.特别地,我们获得此类问题的Green函数,使问题的解决更直观和简单. 相似文献
18.
<正> 引言 不可微分的連續函數,已經有了很多有名的例子.但是都多少有些困難,不能為初學者所接受.筆者最近發現一個這種函數的例子.除函數概念,連續性與可微分性等幾個必要的概念外,不需要其他的理論. 相似文献
19.
本文讨论四阶常微分方程$x^{(4)}(t)=f(t,x(t),x'(t),x'(t),x'(t)),\;\;\;t\in(0,1), \eqno (E)$在边值条件$x(0)=x(1)=0,\;\alpha x'(\xi_1)-\beta x'(\xi_1)=0,\;\gamma x'(\xi_2)+\delta x'(\xi_2)=0, \eqno(B)$满足共振情形: $\alpha \delta+\beta\gamma+\alpha\gamma(\xi_2-\xi_1) 相似文献
20.
We are concerned with the nonlinear Schrodinger-Poisson equation{-△u+(V(x)-λ)u+φ(x)u = f(u),(P)-△ φ = u2,limx|→+∞ φ(x)= 0,x∈ R3,where λ is a parameter,V(x)is an... 相似文献