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1.
宋雪  杨赟瑞  杨璐 《应用数学和力学》2022,43(10):1164-1176
研究了一类带有外部输入项的时间周期SIR传染病模型周期行波解的存在性和不存在性.首先,通过构造辅助系统适当的上下解并定义闭凸锥,将周期行波解的存在性转化为定义在这个闭凸锥上的非单调算子的不动点问题,利用Schauder不动点定理建立辅助系统周期解的存在性,并利用Arzela-Ascoli定理证明了原模型周期行波解的存在性.其次,借助分析技术得到了周期行波解的不存在性.  相似文献   

2.
研究了Liénard方程的一类新的等价系统解的有界性与周期解的存在性.证明了几个比较定理,使传统Liénard方程等价系统解的有界性和周期解的存在性可用于判定新等价系统解的有界性与周期解的存在性.  相似文献   

3.
研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.  相似文献   

4.
研究了一类含参泛函微分方程反周期解的存在性.获得了当参数在一定范围取值时反周期解的存在性结果,得到了反周期解存在的充分条件,并通过例子表明结果的可行性.主要工具为Leray-Schauder非线性抉择.  相似文献   

5.
该文利用Schauder和Roth不动点定理,讨论了一类高维非自治系统周期解的存在性和唯一性,给出了其存在周期解和存在唯一周期解的一组充分性判据.  相似文献   

6.
讨论了一类鞍点型线性半连续动力系统,给出了阶1周期解存在性、唯一性、稳定性以及阶2周期解不存在性的条件,并指出在一定的条件下,系统可以存在无穷多个阶1周期解.最后给出了相应理论结果的数值模拟.  相似文献   

7.
利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.  相似文献   

8.
二阶非线性差分方程多重周期解的存在性   总被引:1,自引:0,他引:1  
本文研究了一类带参数非自治的二阶非线性差分方程多重周期解的存在性问题.利用Morse理论,建立了此类方程多重周期解的存在性准则.  相似文献   

9.
利用重合度理论中的延拓定理研究非自治周期食饵—捕食系统的非平凡周期解存在性,给出了周期解存在的充分条件.  相似文献   

10.
研究了一类具无穷时滞的中立型周期微分系统周期解的存在性问题.利用指数型二分性及Krasnoselskii不动点定理,建立了保证该系统的周期解的存在性的充分条件.所得结果推广了文[1-7]的有关结果.  相似文献   

11.
In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here.  相似文献   

12.
研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.  相似文献   

13.
This paper is concerned with the existence and asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a planktonic competition model under Dirichlet boundary conditions. The approach to the problem is by the method of upper and lower solutions and the bootstrap argument of Ahmad and Lazer. It is shown under certain conditions that this system has positive or semi-positive periodic solutions. A sufficient condition is obtained to ensure the stability and global attractivity of positive periodic solutions.  相似文献   

14.
We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

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15.
共振条件下一类方程无界解和周期解的共存性   总被引:1,自引:1,他引:0  
讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性.利用Poincare映射轨道的性质,给出了无界解的存在性条件.在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的.最后,给出了一个无界解和周期解共存的具有等时位势的方程实例.  相似文献   

16.
We study stability of antisymmetric periodic solutions to delay differential equations. We introduce a one-parameter family of periodic solutions to a special system of ordinary differential equations with a variable period. Conditions for stability of an antisymmetric periodic solution to a delay differential equation are stated in terms of this period function.  相似文献   

17.
Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross–Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the 1D stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov–Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.  相似文献   

18.
In this note, we study a discontinuous three-term recurrence relation which arises from seeking the steady states of a cellular neural network with step control function. Several collections of periodic solutions are found. A necessary and sufficient condition for a solution to be periodic is stated and aperiodic solutions are found as consequences. We also show that any periodic solution can be derived from a primary periodic solution with least period not divisible by 5. Although the periodic or aperiodic solutions we found are not exhaustive, they are quite abundant and may reflect some of the rich physical phenomena in true biological systems. Our method in this note may also provide a general approach to analyze the periodicity of solutions of similar recurrence relations.  相似文献   

19.
In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.  相似文献   

20.
In this paper, using Fourier series, we study the problem of the existence of periodic solutions of a type of periodic neutral differential difference system. Some necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional equation system are obtained, and at the same time, we present a method with formula shows how to find the periodic solutions.  相似文献   

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