共查询到20条相似文献,搜索用时 78 毫秒
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本文研究一类含非定线性项的二阶Hamilton系统多周期解问题.在位势函数满足超二次齐次条件下,利用临界点理论中对称型越山定理,证明了系统存在无穷多个给定周期的周期解. 相似文献
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利用度理论研究了二阶Liénard方程反周期解的存在性和二阶Duffing方程具有对称性的反周期解的存在性,改进了一些已有的结果. 相似文献
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考虑耗散效应的金属杆受扰动后的非线性动力学现象分析 总被引:2,自引:1,他引:1
研究在周期外载荷作用及Neumann边界条件下,考虑Peierls-Nabarro效应的有限长一维金属杆的运动,以位移表达杆的控制方程,是受扰动的类sine-Gordon方程.利用空间四阶精度,时间二阶精度的有限差分格式模拟系统的动力响应.对于一定特征尺寸及物理性质的金属杆,研究了初始呼吸子及周期载荷幅值对杆动力行为的影响,结果显示了4种典型的动力行为:与空间位置无关的简谐运动、单波的简谐运动、单波的准周期运动和单空间模态的时间混沌运动.通过Poincaré截面和功率谱确定系统的运动特征. 相似文献
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二阶离散Hamiltonian系统的多重周期解 总被引:2,自引:0,他引:2
利用变分原理和Clark定理,研究了带参数的二阶离散Hamiltonian系统的多重周期解,得到了此类方程周期解个数的下界估计. 相似文献
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我们利用Ambrosetti-Rabinowitz对称形式的山路引理证明了给定周期T的对称超二次二阶哈密尔顿系统具有无穷多个反T/2-周期且奇的周期解. 相似文献
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具逐段常变量中立型时滞微分方程的概周期解 总被引:6,自引:0,他引:6
袁荣 《数学年刊A辑(中文版)》1998,(4)
通过构造二阶差分方程的概周期序列解,研究了中立型时滞逐段常变量微分方程概周期解的存在性. 相似文献
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本文研究一类具新的超二次条件的二阶Hamiltonian系统周期解问题,利用同调环绕理论和Morse理论得到一些周期解的存在性结论. 相似文献
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This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann–Liouville and Caputo definitions, we discuss when the fractional derivative and when the fractional integral of a certain class of periodic functions satisfies particular properties. We study concepts close to the well known idea of periodic function, such as S-asymptotically periodic, asymptotically periodic or almost periodic function. Boundedness of fractional derivative and fractional integral of a periodic function is also studied. 相似文献
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We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions. 相似文献
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Qualitative Analysis and Periodic Cusp Waves to a
Class of Generalized Short Pulse Equations 下载免费PDF全文
In this paper, we qualitatively study periodic cusp waves to a class
of generalized short pulse equations, which are of the general form of three
special generalized short pulse equations, from the perspective of dynamical
systems. We show the existence of smooth periodic waves, periodic cusp wave
and compactons, obtain exact expression of periodic cusp wave and illustrate
the limiting process of periodic cusp wave from smooth periodic waves. 相似文献
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Alexandr Fischer 《Applications of Mathematics》2004,49(3):269-284
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid. 相似文献
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Lienard方程周期解、概周期解的存在性 总被引:20,自引:2,他引:18
本文考虑Lienard方程x”十f(x)x’+g(x)=e(t),我们得到:当且时,对于任意周期或概周期。数e(t),它有周期或概周期解.而对于Lienard方程x”+f(x)x’+cx=e(t),我们得到:当c>0且时,对于任意周期、或概周期函数e(t),它有周期或概周期解. 相似文献
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利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的. 相似文献
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基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件.并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟. 相似文献
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This paper is concerned with a class of periodic degenerate parabolic system with time delays in a bounded domain under mixed boundary condition. Under locally Lipschitz condition on reaction functions, we apply Schauder fixed point theorem to obtain the existence of periodic solutions of the periodic problem. With quasi-monotonicity in addition, we also show that the periodic problem has a maximal and a minimal periodic solutions. Applications of the obtained results are also given to some nonlinear diffusion models arising from ecology. 相似文献