共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove an abstract and flexible continuation theorem for zeros of parametrized Fredholm maps between Banach spaces. It guarantees not only the existence of zeros to corresponding equations, but also that they form a continuum for parameters from a connected manifold. Our basic tools are transfer maps and a specific topological degree. The main result is tailor-made to solve boundary value problems over infinite time-intervals and for the (global) continuation of homoclinic solutions. 相似文献
2.
Bing-wen Liu~ Li-hong Huang~ Department of Mathematics Hunan University of Arts Science Changde Hunan China College of Mathematics Econometrics Hunan University Changsha China 《应用数学学报(英文版)》2005,(1)
By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Lienard-type equation Our results extend and improve some known results in the literature. 相似文献
3.
Oleg Makarenkov Paolo Nistri 《Journal of Mathematical Analysis and Applications》2008,338(2):1401-1417
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x0 as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem. 相似文献
4.
In this paper we prove a result on the existence of periodic motions for the periodically forced Liénard differential equation
x
″+f(x)x
′+g(x)=e(t) in a situation where the phase portrait of the associated autonomous equation is similar to that of a centre limited by
an unbounded separatrix. The existence result, which is based on a degree theoretic continuation theorem, enables us to treat
some interesting cases not previously considered in the literature.
Received: April 27, 2000 Published online: December 19, 2001 相似文献
5.
Zhao Yong Han Maoan Yang Junmin 《Annals of Differential Equations》2007,23(4):593-602
In this paper,we are concerned with a cubic near-Hamiltonian system,whose unperturbed system is quadratic and has a symmetric homoclinic loop.By using the method developed in [12],we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop.Further,we give a condition under which there exist 4 limit cycles. 相似文献
6.
7.
一类平面三次微分系统极限环的存在性与唯一性 总被引:4,自引:0,他引:4
蛤出三次系统{dx/dt=-y(ax^2 bx 1) δx-lx^2 dy/dt=x(ax^2 bx 1)极限环的不存在性,存在性及唯一性的一些充分条件. 相似文献
8.
一类二阶Hamiltonian系统的无穷多周期解 总被引:1,自引:0,他引:1
研究一类超线性二阶Hamiltonian系统,且非线性项是奇的,不需要假设Ambros-etti-Rabinowitz的超二次条件,利用对称型山路引理得到无穷多周期解存在性结果. 相似文献
9.
具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性 总被引:6,自引:0,他引:6
§ 1 IntroductionFormanyspeciesthespatialfactorsareimportantinpopulationdynamics .Thetheoreticalstudyofspatialdistributionhasbeenextensivelystudiedinmanypapers .Mostofthepreviouspapersfocusedonthecoexistenceofpopulationsmodelledbyststemsofordinarydiffere… 相似文献
10.
This note is an addendum to the results of Lazer and Frederickson [1], and Lazer [4] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [4] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem. 相似文献
11.
12.
一类具偏差变元的二阶微分方程周期解 总被引:3,自引:0,他引:3
利用Mahwin重合度拓展定理研究了一类具偏差变元的二阶微分方程x^n(t)+f(x’(t))+h(x(t))x’(t)+g(x(t—r(t)))=p(t)周期解问题,得到了周期解存在的一组充分条件. 相似文献
13.
In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials. 相似文献
14.
15.
MOUSSAOUI Abdelkrim KHODJA Brahim 《偏微分方程(英文版)》2009,22(2):111-126
In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
16.
17.
18.
This paper is concerned with periodic solutions of first-order nonlinear functional differential equations with deviating
arguments. Some new sufficient conditions for the existence of periodic solutions are obtained. The paper extends and improves
some well-known results. 相似文献
19.
20.
具有常数输入的非自治SIR流行病模型周期解的存在性 总被引:1,自引:0,他引:1
胡新利 《纯粹数学与应用数学》2007,23(3):372-376,380
利用MAWHIN重合度理论中的延拓定理研究了一类具有常数输入的非自治SIR流行病模型的非平凡周期解的存在性.并用MatLab对其进行了数值模拟,作出了模型的相图和解曲线图形. 相似文献