共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e~(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree. 相似文献
2.
Affine-Periodic Solutions and Pseudo Affine-Periodic Solutions for Differential Equations with Exponential Dichotomy and Exponential Trichotomy 下载免费PDF全文
It is proved that every $(Q,T)$-affine-periodic differential equation has a $(Q,T)$-affine-periodic solution if the corresponding homogeneous linear equation admits exponential dichotomy or exponential trichotomy. This kind of ``periodic'' solutions might be usual periodic or quasi-periodic ones if $Q$ is an identity matrix or orthogonal matrix. Hence solutions also possess certain symmetry in geometry. The result is also extended to the case of pseudo affine-periodic solutions. 相似文献
3.
Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented. 相似文献
4.
Shiwang Ma Zhi-Qiang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(5):1413-1442
In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity. 相似文献
5.
Zhenjie Liu 《分析论及其应用》2009,25(4):369-380
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis
functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence
degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time
scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method
is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference
equations. 相似文献
6.
YU Jianshe & GUO Zhiming College of Mathematics Information Sciences Guangzhou University Guangzhou China 《中国科学A辑(英文版)》2006,49(10):1303-1314
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established. 相似文献
7.
《Mathematical and Computer Modelling》2007,45(7-8):974-980
First, a general theorem on the existence of periodic solutions for equations with small discrete delay is obtained by employing a technique which is based on a result of the existence of inertial manifold for small discrete delay equation, meanwhile, this general theorem is applied to show the existence of periodic solution for a predator–prey system with small discrete delay. Second, this technique is also used to obtain the existence of travelling wave solution for a host–vector disease model with small discrete delay. 相似文献
8.
Yu TongZhenjie Liu Zhiying GaoYonghong Wang 《Communications in Nonlinear Science & Numerical Simulation》2012,17(8):3360-3366
In this paper, we systematically investigates the existence of periodic solutions of a predator-prey system with sparse effect and Beddington-DeAngelis or Holling III functional response on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the systems. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. 相似文献
9.
Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time
《Journal of Computational and Applied Mathematics》2006,188(2):256-264
In this paper, we employ the Mawhin's continuation theorem to study the existence of positive periodic solutions of the nonautonomous periodic model of population with continuous and discrete time. It is interesting that the conditions to guarantee the existence of positive periodic solutions of discrete time model are similar to those for the corresponding continuous time model. 相似文献
10.
利用变分法获得了一类二阶微分方程异宿解存在的一个充分条件.将连续情况下的二阶微分方程异宿解研究推广到离散情况下来研究. 相似文献
11.
Blaise Kone 《Journal of Difference Equations and Applications》2013,19(10):1537-1547
In this paper, we prove the existence and uniqueness of weak solutions for a family of discrete boundary value problems for data f which belong to a discrete Hilbert space H. Moreover, as an extension, we prove some existence results of weak solutions for more general data f depending on the solution. 相似文献
12.
路艳琼 《纯粹数学与应用数学》2010,26(6):1012-1020
研究一类二阶离散Neumann边值问题正解的存在性,运用不动点指数理论获得了方程存在正解的最优条件,并给出一个具体例子说明这一结果。 相似文献
13.
In this paper, we investigate the existence of two solutions for second-order discrete Sturm-Liouville boundary value problem with a p-Laplacian. By using critical point theory, the existence of at least two solutions is obtained. 相似文献
14.
A. A. Amosov A. E. Vestfalsky 《Computational Mathematics and Mathematical Physics》2006,46(4):691-718
The Bakhvalov-Eglit two-scale homogenized equations are used to describe the motion of layered periodic compressible media with rapidly oscillating data. A new finite-difference scheme for a system of such equations is proposed and analyzed in the case of a thermoviscoelastic Voigt-type body. A priori estimates of solutions are derived for nonsmooth data. The existence and uniqueness of discrete solutions are established. A theorem is proved on the convergence of a subsequence of discrete solutions to a weak solution of the problem under study. Simultaneously, a new theorem on the existence of global weak solutions is deduced. 相似文献
15.
Abderrazek Karoui Amara Ammari Belgacem Selmi 《Journal of Fourier Analysis and Applications》2007,13(5):533-550
In this work, we study the existence of solutions of the deconvolution problems in the discrete setting. More precisely, we
prove the existence of solutions of the discrete multichannel deconvolution problems DMDP with convolvers being the characteristic
functions of finite sets of positive integers. Also, we provide the reader with a simple method and a fast algorithm for finding
the closed forms of the discrete deconvolvers with minimal supports that constitute exact solutions of the DMDP. Moreover,
we show that unlike the singular value decomposition scheme, the multichannel deconvolution scheme based on the use of these
discrete deconvolvers is not very sensitive to small 2-norm perturbation of the data. Finally, we show how to generalize our
method for solving the 2-D version of the DMDP. 相似文献
16.
时间测度上具有Holling-N类功能反应和扩散的捕食系统的周期解 总被引:1,自引:0,他引:1
在时间测度上研究了一类具有Holling-N类功能反应和扩散的捕食系统,利用Mawhin重合度理论建立了这类系统周期解存在的一些新的充分性判据,从而使这一类系统的连续与离散情形,即相应的微分方程和差分方程的周期解存在性问题得到了统一. 相似文献
17.
本文在时标上运用迭合度理论中的Gaines和Mawhin连续性定理研究了一类非自治捕食系统的周期解的存在性,得到了此模型周期解存在的充分条件,该方法可将证明连续和离散微分方程的周期解的存在性统一起来. 相似文献
18.
时间测度上具有时滞基于半比率的捕食者-食饵扩散系统的周期解 总被引:1,自引:0,他引:1
刘振杰 《数学的实践与认识》2008,38(24)
在时间测度上研究一类具有时滞和基于半比率且有功能性反应的两种群捕食者-食饵扩散系统,利用Mawhin重合度理论建立了这类系统的周期解存在的一个充分性判据.从而使这一类系统的连续与离散情形即相应的微分方程和差分方程的周期解存在性问题得到了统一研究. 相似文献
19.
研究了一类具有比率型功能反应的食物链时标动力学系统,利用重合度理论中的延拓定理讨论了此系统周期解的存在性问题,得到了保证周期解存在的充分条件,从而使这一类系统的连续与离散情形:微分方程和差分方程的周期解存在性问题得到了统一研究. 相似文献
20.
应用离散泛函分析方法证明了非线性抛物型方程组的隐格式离散向量解的收敛性,同时得到微分方程组弱解的存在性. 相似文献