共查询到20条相似文献,搜索用时 15 毫秒
1.
Changrong Zhu Guangping Luo Kunquan Lan 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation manifolds, the perturbed system has various coexistence of homoclinic solutions which are linearly independent. 相似文献
2.
We consider the persistence of a transversal homoclinic solution and chaotic motion for ordinary differential equations with a homoclinic solution to a hyperbolic equilibrium under an unbounded random forcing driven by a Brownian force. By Lyapunov–Schmidt reduction, the persistence of transversal homoclinic solution is reduced to find the zeros of some bifurcation functions defined between two finite spaces. It is shown that, for almost all sample paths of the Brownian motion, the perturbed system exhibits chaos. 相似文献
3.
The problem of bifurcation from homoclinic solution towards periodic solution was considered for weekly coupled singular systems. By using functional analytic approach based on the Lyapunov–Schmidt reduction, we obtained some functions H:Rd-1×R→Rd. The simple roots of the equations, H(α,β)=0, correspond to the existence of subharmonic solutions. And if the vector field is 2-period, then for any integer m , the weakly coupled singular system has 2m-period solution. 相似文献
4.
Transverse homoclinic orbit bifurcated from a homoclinic manifold by the higher order melnikov integrals 下载免费PDF全文
Consider an autonomous ordinary differential equation in $\mathbb{R}^n$ that has a $d$ dimensional homoclinic solution manifold $W^H$. Suppose the homoclinic manifold can be locally parametrized by $(\alpha,\theta) \in \mathbb{R}^{d-1}\times \mathbb{R}$. We study the bifurcation of the homoclinic solution manifold $W^H$ under periodic perturbations. Using exponential dichotomies and Lyapunov-Schmidt reduction, we obtain the higher order Melnikov function. For a fixed $(\alpha_0,\theta_0)$ on $W^H$, if the Melnikov function have a simple zeros,
then the perturbed system can have transverse homoclinic solutions near $W^H$. 相似文献
5.
Cheng-yue Li 《高校应用数学学报(英文版)》2009,24(1):49-55
This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation
u^(4)+pu″+a(x)u-b(x)u^2=c(x)u^3=3
arising in the study of pattern formation by means of Mountain Pass Lemma. 相似文献
u^(4)+pu″+a(x)u-b(x)u^2=c(x)u^3=3
arising in the study of pattern formation by means of Mountain Pass Lemma. 相似文献
6.
利用重合度理论和一些分析技巧,得到一类二阶时滞Duffing微分方程的2kT周期解,通过对该微分方程的一系列周期解取极限获得同宿解的存在性.同时,β(t)是可变号的. 相似文献
7.
The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations 下载免费PDF全文
Omar Abu Arqub 《Mathematical Methods in the Applied Sciences》2016,39(15):4549-4562
The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of differential algebraic systems for ordinary differential equations. The reproducing kernel Hilbert space is constructed in which the initial conditions of the systems are satisfied. While, two smooth kernel functions are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
§ 1 IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up, x∈ R,( 1 )where1
相似文献
9.
运用二分性及压缩映射原理,研究一类时滞三阶微分方程概周期解的存在性,得到此类微分方程的概周期解存在的充分性定理. 相似文献
10.
Dynamical understanding of loop soliton solution for several nonlinear wave equations 总被引:1,自引:0,他引:1
Ji-bin LI Department of Mathematics Zhejiang Normal University Jinhua China Kunming University of Science Technology Kunming China 《中国科学A辑(英文版)》2007,50(6):773-785
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution. 相似文献
11.
Shi Ping Lu 《数学学报(英文版)》2012,28(6):1261-1274
By means of Mawhin’s continuation theorem and some analysis methods, the existence of 2kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set. 相似文献
12.
Gani Stamov 《Applicable analysis》2013,92(1-2):45-56
Sufficirnt condition for the existence of almost periodic solutions of forced perturbed systems of impulsive differential equations with impulsive effect at fixed Moments are considered. 相似文献
13.
一类非线性微分方程的概周期解 总被引:1,自引:0,他引:1
运用Leray-Schauder不动点定理和Liapunov函数方法,研究了一类非线性微分方程的概周期解,得到了该微分方程概周期解存在的充分条件. 相似文献
14.
15.
W.M. Wright 《Numerical Algorithms》2001,26(2):123-130
Diagonally Implicit Multistage Integration Methods (DIMSIMs) of type 1 and 2 have considerable potential as numerical algorithms for ordinary differential equations. The aim of this paper is to construct such methods of order 4 of type 1 and 2, which completes the set for orders 1–8. 相似文献
16.
17.
In this paper, we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation
x′(t)=α(t)x(t)-β(t)x2(t)+γ(t)x(t-τ(t))x(t). 相似文献
18.
Existence of almost periodic solutions for strong stable impulsive differential equations 总被引:1,自引:0,他引:1
Conditions for strong stability and the existence of almostperiodic solutions of systems of impulsive differential equationswith impulsive effect at fixed moments are obtained. The investigationsare carried out by means of piecewise continuous functions whichare analogues of Lyapunov functions. 相似文献
19.
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases. We then use the argument of the relative compactness of Wiener-Sobolev spaces in C0([0,T],L2(Ω)) and generalized Schauder?s fixed point theorem to prove the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations. The condition on F is then further weakened by applying the coupling method of forward and backward Gronwall inequalities. The results are also valid for stationary solutions as a special case when the period τ can be an arbitrary number. 相似文献
20.
In this paper, a class of stochastic functional differential equations given by