共查询到20条相似文献,搜索用时 78 毫秒
1.
一类高维时滞微分方程的周期解 总被引:10,自引:0,他引:10
本文考虑高维时滞微分方程x′(t)=A(t,x(t))x(t)+f(t,x(t-r(t)))其中(t,x)∈Rn,A(t,x)是n×n连续矩阵,f(t,x)是n维连续向量,r(t)是时间依赖的滞量,应用不动点定理,在确定的条件下,证明了该系统的周期解的存在性与唯一性 相似文献
2.
指数型二分性和周期系统的周期解 总被引:4,自引:0,他引:4
陈凤德 《纯粹数学与应用数学》1999,15(1):18-24
先讨论指数型二分性成立的条件,在某种意义下推广了Lazer关于二分性的结果,之后,我们用该结论探讨Lasota-Opiul方程及方程x=f(t,x),f(t+w,x)=f(t,x),f(t,x)∈C’(R*R^n,R^n)的周期解的存在性,推广了文「2」的主要结果,并得到一些新的结果。 相似文献
3.
颜跃新 《高校应用数学学报(A辑)》1999,14(2):135-139
本文主要研究了强迫振动方程:x+(f(x)+g(x)x)X+h(x)=e(t)的解的有界性以及周期解的存在性,这里f(x),g(x),h(x)在(-∞,+∞)中连续,e(t)在「0,+∞)上连续,得到了解的有界性与存在周期解的条件。 相似文献
4.
函数f(x)=|sinβx/sinαx|(α,β>0)的周期性曾丕刚陕西省镇安县中学711500定理函数f(x):为周期函数的充要条件是为周期函数,L为周期.(2)若f(X)是周期函数,设t(t>0)是它的周期,则f(x+t)=f(X),即在定义域内... 相似文献
5.
一类微分差分方程的周期解 总被引:1,自引:0,他引:1
本文研究微分差分方程x'(t)=-f(x(t),x(t-τ1))-f(x(t),x(t-τ2))-...-f(x(t),x(t-τn))非平凡周期解的存在性问题,得到了一些判别准则,推广和改进了文[1-4]的工作。 相似文献
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7.
本刊1997年第3期《利用一次函数的保号性解题》一文给出,一次函数f(x)=kx+b具有如下一条性质(A≥0):如果|f(m)|>A,|f(n)|>A,则x∈[m,n]时,有|f(x)|>A.我们指出,这一结论是错误的.例如,取f(x)=x,有|f(... 相似文献
8.
设n≥3,定义Tf(x,xn)=P.V.∫R^n-1b(t)K(t)f(x=t,xn-Г(│t│))dt,其中x∈R^n-1,b(t)为R^n-1上的有界函数,K(t)为R^n-1上满足Hormander条件的函数,且Г(s)为〔0,∞)上的任意函数。本文给出了T为(L∞(R^n),BMO(R^n))一型,或等价地(H^1(R^n),L^1(R^n))一型时,b所应满足的充分必要条件。 相似文献
9.
最佳L2局部逼近存在唯一的充分必要条件 总被引:1,自引:0,他引:1
本文给出了最佳L2局部逼近的存在唯一性定理,设f∈L2(0,δ),Sn=span(u0,u1,...Un-1)C^n-1(0,δ),且detWn(u0,u1,...un-1;0)≠0,那么,当x→0时,网(Px(f,Sn)收敛于Sn中某元素P0(f,Sn)的充要条件为:f=Pn-1+h,其中Pn-1(t)=n-1∑i=1aiti(h,1)x=0(X^n),x→0,且P0(f,Sn)=UW^-1nA 相似文献
10.
薛留根 《数理统计与应用概率》1994,9(3):54-60
设(Xn)是R^1中的平稳,强混合序列,具有公共的密度f(x),则可定义f(x)及其导函数f^(r)(x)的核估计与最近邻估计f^(r)n(x)=(nh^r+1n(x))^-1n∑i=1K^(r)(Xi-X/hn(x)),fn(x)=(nan(x))^-1n∑i=1K(Xi-x/an(x))其中核函数K(X)为取定的概率密度函数,且具有r(r≥0)阶导数,窗宽hn(x)=hn(x;X1,...,X 相似文献
11.
Litan Yan 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):47-56
Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 . 相似文献
12.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):171-191
We give sufficient conditions for a family Z, e > 0 of continuous finite variation processes to converge weakly to a diffusion process Z. Then we consider the integral equation dXE(t) = (l)(Xe(t))dZE{t) and the stochastic equation dX{i) = (j)(X{t))dZ{t) and denote by X(t,x,w respectively X{t,x,(jo), the solution starting at x. We prove that PoX~l, e>0 converge weakly to Pol 相似文献
13.
51. Introduction and Statement of ResultsLet X ~ {Xt, t 2 0} be a standajrd d-dimensional Brownian motion with drift c startedat fiXed XO ~ x:Xo ~ Wb ct, t 2 0,where Wt is the standard d--dimensional Brownian motion, c E R'(d 2 2) is a fixed vector.Denote by P:(.) the probability meajsure on the path space of X corresponding to initialstate XO = x and drift vector c, with E;(.) the corresponding expection operator. Forsimplity, we shall write Pz(.) and Ex(.) to refer to the case c ~ … 相似文献
14.
Lienard方程周期解、概周期解的存在性 总被引:20,自引:2,他引:18
本文考虑Lienard方程x”十f(x)x’+g(x)=e(t),我们得到:当且时,对于任意周期或概周期。数e(t),它有周期或概周期解.而对于Lienard方程x”+f(x)x’+cx=e(t),我们得到:当c>0且时,对于任意周期、或概周期函数e(t),它有周期或概周期解. 相似文献
15.
吴建国 《数学的实践与认识》2008,38(17)
设(Xi,Yi)(i=1,2,…,n)是来自总体(X,Y)的样本(独立同分布),其中X∈R1,Y∈Rq.M(x y)是Y=y时X的条件分布,Mnkn(x y)为M(x y)的第kn个最近邻域的经验分布估计量,讨论条件经验过程Sn(t,x,y)=kn12(Mnkn(x y)-M(x y))的渐近性质,得出在适当条件下,对固定的y,Sn(t,x,y)(x,t为参数)弱收敛于某一G aussian过程S(.). 相似文献
16.
A theorem on asymptotic equilibrium is proved for the solutions of the system(1)X n=f(t,X), x t 0=xo where f(t,x) is majorized by a funciton g(t,u) which is non-increasing in u. It is of interest to notice that the funcitons f(t,x) and g(t,u) need not be defined for x=0 and u=0 respectively. Such majorant functions occur in gravitational problems and therefore the result is of pracitcal interest.Using this, the asymptotic relatiohship between the solutions of(2)y=A(t)y, y t o=yoand its nonlinear perturbation(3) X=A(t)x+f(t,x), Xt o is investigated. This last result includes as a special case two theorems of Hallam[2] 相似文献
17.
Potential Analysis - Given the pair of vector fields X = ?x + |z|2my?t and Y = ?y ?|z|2mx?t,where (x,y,t) = , we give a condition on a bounded domain which ensures... 相似文献
18.
W. E. Fitzgibbon 《Annali di Matematica Pura ed Applicata》1976,110(1):279-293
Summary Let X be a Banach space and {A(t)|t ε [0, T]} a family of closed linear, densely defined m-accretive operators in X. This
paper is concerned with the additive perturbation of {A(t)|t ε [0, T]} by a continuous family of nonlinear accretive operators
{B(t)|t ε [0, T]}. Namely solutions are provided for the integral equation u(t, τ, x) = W(t, τ)x −
W(t, s)B(s) · · u(s, τ, x)ds, u(τ, τ, x) = x where W(t, s) is the linear evolution operator associated with the linear differential
equation v'(t, s, x) + A(t)v(t, s, x) = 0, v(s, s, x) = x.
Entrata in Redazione il 30 luglio 1975. 相似文献
19.
1MainResultsConsidersystem11~.x f(x)x' g(x)~0(1)wheref(x)islocallyintegrable,g(x)isdifferentiablealldg(0)=0.Theroem1Thezerosolutionofsystem(1)isuniformlyasymptoticallystableifbyequivalenttransf'Ormu=xov=X' F(x).DefineW[t,(uif\v)]j6ug(s)ds Iv',thenwisaposi… 相似文献
20.
Brown运动的逗留时与首中时 总被引:1,自引:0,他引:1
设为中的标准Brown运动,对0<α,记本文求出了X在首中球面之前逗留在Bα内的时间的Laplace变换,在首中之前逗留在Bαb内的时间的Laplace变换以及在首中之前逗留在Bαb内的时间的Laplace变换.作为推论,求出了X关于球面首中时的Laplace变换,逗留在球内总的时间的Laplace变换及逗留在球壳内的总的时间的LaPlace变换. 相似文献