共查询到20条相似文献,搜索用时 62 毫秒
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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
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反周期解问题是非线性微分系统动力学的重要特征.近年来,非线性整数阶微分系统的反周期解问题得到了广泛的研究,非线性分数阶微分系统的反周期解问题也得到了初步的讨论.不同于已有的工作,该文研究时不变分数阶系统反周期解的存在性问题.证明了时不变分数阶系统在有限时间区间内不存在反周期解,而当分数阶导数的下限趋近于无穷大时,时不变分数阶系统却存在反周期解. 相似文献
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张无畏 《高校应用数学学报(A辑)》1999,14(1):2
本文研究了两类分段对称系统周期解的存在性,得到了系统相应的周期解存在的充分条件.作为应用,证明了一类具有分段对称性的时滞微分方程的周期解的存在性,推广了现有的相关结果. 相似文献
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本文建立了系统解一致稳定、解一致渐近稳定和某种Liapunov函数存在的充要条件,并且得到:满足Lipschitz条件而且解一致渐近稳定的概周期系统有唯一的概周期解,周期系统有唯一的周期解。 相似文献
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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
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本文研究了非自治Ayala模型的概周期和周期系统,我们得到在一定条件下,其概周期系统存在唯一全局吸引的概周期解且其概周期解在壳扰动下是稳定的。在与概周期情形类似的条件下我们得到其w-周期系统存在唯一全局吸引的w-周期解。 相似文献
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吴晓非 《数学物理学报(A辑)》1998,(Z1)
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
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该文运用周期抛物型算子理论,Schauder估计和分歧理论讨论了一类周期反应扩散方程,即带扩散项捕食-食饵系统的周期解的存在性,得出了系统正周期解存在的充要条件. 相似文献
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In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified Kd V–KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions. 相似文献
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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
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Vladimir Ivanovich Mironenko Vladimir Vladimirovich Mironenko 《Journal of Applied Analysis & Computation》2016,6(3):876-883
In the paper we are giving the new method for searching periodic solutions of periodic differential systems. For this we construct a differential system with the same Reflecting Function as the Reflecting Function of the given system and with a known periodic solution. Then the initial data of the periodic solutions of this two systems coincide. In such a way the problem of existance periodic solutions goes to the Cauchy problem. 相似文献
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The method of upper and lower solutions is a classical tool in the theory of periodic differential equations of the second order. We show that this method does not have a direct extension to almost periodic equations. To do this we construct equations of this type without almost periodic solutions but having two constants as ordered upper and lower solutions. 相似文献
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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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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
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高维时滞周期的Kolmogorov型系统的正周期解 总被引:27,自引:0,他引:27
本文应用Banach空间中的Horn不动点得到了高维时滞的周期Kolmogorov型生态系统的正周期解存在性定理,作为这个定理的应用,讨论了几类时滞的周期LotkaVolterra型系统的正周期解的存在性问题,建立了新的实用的判别准则。 相似文献
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考查了周期边界条件下的磁流体方程,证明了它的解关于时间是解析的,由此得到了磁流体方程的解的向后惟一性.对于周期解,证明了当周期小于某个常数时,周期的弱解是强解,进一步地这样的强解是定常解. 相似文献