共查询到20条相似文献,搜索用时 31 毫秒
1.
Jerzy Jezierski 《数学学报(英文版)》2014,30(9):1477-1494
There are two algebraic lower bounds of the number of n-periodic points of a self-map f :M → M of a compact smooth manifold of dimension at least 3:N Fn(f) = min{#Fix(gn); g ~f; g is continuous} and N J Dn(f) = min{#Fix(gn); g ~ f; g is smooth}.In general,N J Dn(f) may be much greater than N Fn(f).If M is a torus,then the invariants are equal.We show that for a self-map of a nonabelian compact Lie group,with free fundamental group,the equality holds all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1. 相似文献
2.
In this paper, K-controllability and approximate K-controllability of non- linear neutral differential equations in Banach spaces are studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using Leray-Schauder theory. 相似文献
3.
Jian Lin Li 《数学学报(英文版)》2013,29(7):1323-1328
For positive integers N1 , N2 , . . . , Nn , let L = Zn + A and Λ = N1Z ×···× NnZ + Γ be two rational periodic sets, where A(1/N1 )Z ×···× (1/Nn)Z and ΓZn are finite sets with (A-A) ∩ Zn = {0} and (Γ-Γ) ∩ (N1Z ×···× NnZ) = {0}. In this note, we shall determine conditions under which the tiling set L has universal spectrum Λ. We first obtain a criterion of universal spectra. This criterion combined with the properties of compatible pair yields many necessary and sufficient conditions for Λ to be a universal spectrum for L. We then show that, under some mild additional conditions, the conjecture of Lagarias and Szabó is true. The results here extend the corresponding results of Lagarias, Szabó and Wang. 相似文献
4.
LIU YUAN-YUAN CHAI ZHEN-HUA 《数学研究通讯:英文版》2014,(3):207-221
This paper is concerned with the bifurcation properties on the line of discontinuity of planar piecewise smooth systems. The existence of equilibria and periodic solutions with sliding motion in a class of planar piecewise smooth systems with 3-parameters is investigated in this paper using the theory of differential inclu-sion and tools of Poincar′e maps. 相似文献
5.
In this paper, we discuss the concept of fixed point curve for linear interpolations of weakly inward contractions and establish necessary condition for a nonex- pansive mapping to have approximate fixed point property. 相似文献
6.
ZHANG LEI ZHENG QING-YU SHI SHAO-GUANG 《数学研究通讯:英文版》2014,(3):257-264
The aim of this paper is to set up the weighted norm inequalities for commutators generated by approximate identities from weighted Lebesgue spaces into weighted Morrey spaces 相似文献
7.
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0. 相似文献
8.
近似周期时间序列具有近似的周期趋势,即近似周期性.所谓近似周期性是指它看起来有周期性,但是每个周期的长度不是常数,比如太阳黑子数序列.近似周期时间序列在社会经济现象建模中有着广泛的应用前景.对于近似周期时间序列,关键在于刻画它的近似周期趋势,因为一旦近似周期趋势被刻画出来它就可以作为一个普通的时间序列来处理.然而,关于近似周期趋势刻画的研究却很少. 本文首先建立一些必要的理论,特别地,提出了带长度压缩的保形变换概念,并且得到了带长度压缩的线性保形变换的充分必要,然后基于此理论作者提出了一种估计尺度变换的方法,该方法可以很好地估计出近似周期趋势.最后,对一个仿真实例进行了分析.结果表明,本文所提出的方法强力有效. 相似文献
9.
Anar T. Assanova Narkesh B. Iskakova Nurgul T. Orumbayeva 《Mathematical Methods in the Applied Sciences》2020,43(2):881-902
A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained. 相似文献
10.
S. Sobolevsky 《Studies in Applied Mathematics》2004,112(3):227-234
In this paper we consider nonlinear ordinary differential equations y ( n ) = F ( y ', y , x ) of arbitrary order n ≥ 3 , where F is algebraic in y , y ' and locally analytic in x . We prove that for n > 3 these equations always admit movable branch points. In the case n = 3 these equations admit movable branch points unless they are of the known class y '= a ( x )( y ')2 + ( b 2 ( x ) y 2 + b 1 ( x ) y + b 0 ( x )) y '+ ( c 4 ( x ) y 4 + c 3 ( x ) y 3 + c 2 ( x ) y 2 + c 1 ( x ) y + c 0 ( x )) , where a , bj , cj are locally analytic in x . 相似文献
11.
Anna Capietto Jean Mawhin Fabio Zanolin 《NoDEA : Nonlinear Differential Equations and Applications》1995,2(2):133-163
We prove a continuation theorem for the solvability of the coincidence equationLx=Nx in normed spaces. Applications are given to the periodic boundary value problem for second order ordinary differential equations. Dealing, in particular, with the periodically forced Duffing equation
相似文献
12.
On the existence of periodic solutions for the third-order nonlinear ordinary differential equations 总被引:4,自引:0,他引:4
HuangXiankai 《高校应用数学学报(英文版)》1999,14(2):125-130
In this paper,the existence of periodic solution for the third-order nonlinear ordinarydifferential equation of the form -^x f(-^x) g(-^x) h(x)=p(t) is consldered,where f,g,h andp are the continuous functlons, and p (t T) =p (t). By using the Leray-Schauder degreemethod,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained. Some previous results are extended and improved. 相似文献
13.
Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation 总被引:1,自引:0,他引:1
Maitree Podisuk Ungsana Chundang Wannaporn Sanprasert 《Applied mathematics and computation》2007,190(2):1438-1444
Adam–Bashforth method and Adam–Moulton method are two known multi-step methods for finding the numerical solution of the initial value problem of ordinary differential equation. These two methods used the Newton backward difference method to approximate the value of f(x,y) in the integral equation which is equivalent to the given differential equation. 相似文献
14.
Li-Qing Zhang 《计算数学(英文版)》1992,10(2):147-154
A spline collocation method is proposed to approximate the periodic solution of nonlinear ordinary differential equations. It is proved that the cubic periodic spline collocation solution has the same error bound $O(h^4)$ and superconvergence of the derivative at collocation points as that of the interpolating spline function. Finally a numerical example is given to demonstrate the effectiveness of our algorithm. 相似文献
15.
二个自变量的二阶线性双曲型方程auxx+2buxy+cuyy+dux+euy+g=0,当系数a,b,c,d,e,g满足一定条件时,可以利用变换T:ξ=φ(x,y),η=ψ(x,y)化为一阶线性常微分方程求解,本文给出了求解定理和计算方法. 相似文献
16.
The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations
![]() We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
This paper is concerned with the existence of bounded solutions to the system of equations Xn=anXn−1+ξn, nZ, where ξn are uncorrelated constant variance zero mean random variables. We give necessary and sufficient conditions for boundedness in the general case and then specifically for periodic and almost periodic (an). This provides the first step in extending the periodic autoregressive models, for which boundedness is equivalent to the stationarity of the blocked vector sequence to the almost periodic case. 相似文献
18.
Recently, many authors have studied the following CH-γ equation:ut + c0ux + 3uux - α2(uxxt + uuxxx + 2uxuxx) + γuxxx =0,where α2, c0 and γ are paramters. Its bounded wave solutions have been investigated mainly for the case α2 > 0. For the case α2 < 0, the existence of three bounded waves (regular solitary waves,compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given.In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the case α2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results. 相似文献
19.
We prove using the Faedo-Galerkin method the existence of a generalized solution of an initial-boundary value problem for the non-linear evolution equation
20.
We discuss the existence and the number of periodic solutions of differential equation dx/dt=A1(t)x A2(t)x^2 A3(t)x^3/α0(t) α1(t)x α2(t)x^2 (1)where Ai(t),αj(t)(i=1,2,3;j=0,1,2) are continuous periodic functions.The results of this paper ex-tend the work of paper[1]. 相似文献
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