共查询到20条相似文献,搜索用时 78 毫秒
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洪晓春 《数学的实践与认识》2010,40(3)
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的上界问题,得到了当n≥4时,上界为10n+[n/2]-1. 相似文献
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《数学的实践与认识》2015,(5)
利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分的零点个数估计,得出当n≥5时,上界为10[(4n+1)/3]+4[(4n)/3]+[(4n-1)/3]+13. 相似文献
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利用Picard-Fuchs方程法及Riccati方程法,研究了一类二次可逆系统在任意n次多项式扰动下Abel积分零点个数的线性估计,得到了当n≥3时,上界为4[2n/3]+2[2n+1/3]+[2n+2/3]+16. 相似文献
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一平面可积三次非Hamilton系统的Abel积分 总被引:4,自引:0,他引:4
本文讨论一平面可积三次非Hamilton系统在n次多项式扰动下Abel积分零点个数上确界,得到的结论是该Abel积分的零点个数的上确界为n。 相似文献
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本文讨论一平面Hamilton系统在一般n次多项式扰动下的系统的Abel积分的零点个数估计问题,得到的结论是:该系统的Abel积分的零点个数的上界为[(3n-1)/2]。 相似文献
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利用Abel积分与第一、第二型完全椭圆积分,本文研究一类具有两个中心奇点的平面二次系统在n次小扰动下的Abel积分零点个数上界问题,得到了较小的上界估计. 相似文献
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近年来随机微分方程在数理金融中的应用越来越得到人们的重视,而微分方程的周期性研究对经济模型也越来越重要,Abel(阿贝尔)、Bernoulli(伯努利)方程的周期性具有一定的指导性,但周期性问题的研究常具有一定的难度,为了解决这个问题,采用Mironenko发明的反射函数理论,通过构造与Abel方程、Bernoulli方程共同特征的更一般的方程,得到它们的反射函数,研究了Abel方程与Bernoulli方程的等价性,通过Poincare映射得出了它们相同的周期解问题. 相似文献
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Josep M. Olm Xavier Ros-Oton Tere M. Seara 《Journal of Mathematical Analysis and Applications》2011,381(2):582-589
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x?x−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied. 相似文献
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讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性. 相似文献
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We prove general theorems on mean ergodicity and mean stability
of regularized solution families with respect to fairly general summability
methods. They can be applied to integrated solution families, integrated semigroups
and cosine functions. In particular, through applications with modified
Cesàro, Abel, Gauss, and Gamma like summability methods we deduce particular
results on mean ergodicity and mean stability of polynomially bounded
C0-semigroups and cosine operator functions. 相似文献
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Naeem Alkoumi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5352-5358
New results are proved to estimate the number of periodic solutions of a differential equation of Abel type by using a modification of a technique introduced by Ilyashenko. The main tool is an estimate on the number of zeros of a holomorphic function. A concrete example is analyzed but the results are presented to make the method flexible and applicable to other equations. 相似文献
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一、引言 设G和G′是有限群,G与G′同构与否显然是可以判定的。事实上,若G与G′都是n元有限群,则最坏的情况,要检测G与G′元素之间的n!个1—1映射。对这个问题的处理,文献[1]给出了一个一般方法。 这个方法首先注意到,如果,则必然有G与G′所含周期相同的元素数目相一 相似文献
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For Abel integral equations of the second kind, we investigatethe stability of the collocation method with polynomial splines.We characterize the stability domain in terms of the eigenvaluesof the power series, which arises from the method employed.Furthermore, we prove strong stability and provide a rigorousdiscussion of the boundary of the stability region. A few examplesare considered in more depth and numerical illustrations aregiven. 相似文献
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J. R. Nurcombe 《Proceedings of the American Mathematical Society》1997,125(1):183-187
The definition of generalised Abel summability is extended to positive orders and a definition of strong generalised Abel summability is introduced. A result of Jurkat and Peyerimhoff concerning the implication between Nörlund and generalised Abel summabilities is extended to positive integral order. Analogous results for the corresponding strong methods are also given.
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本文研究二阶非线性微分方程■零解的全局渐近稳定性,其中各函数是实数上的连续函数.我们得到了零解全局渐近稳定的一些充分必要条件和充分条件.推广和改进了文献中的一些结论. 相似文献
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PERIODIC SOLUTION AND ASYMPTOTICITY OF ABEL EQUATION 总被引:1,自引:0,他引:1
Inarticles[1]and[2]theexistenceandstabilityofperiodicsolutionofAbelequation:werediscllsscd,wb')lteth'3coefficientsa(t),b(t),c(t)andd(t)areradalcollt,inuouslyp(3riodicfunctions.111thispal)erwenotonlystudythegeneralI\)rnlofeqllation(A),hiltalsodiscllssitssomespecialcases.FOT'example,as(l(l-)=0l,hcAbelequationbecomesfWeshallobtainsomeinterestingresultsfromit,suchdoubleperiodicsolution,etc.Equation(B)alsohassomeapplication,weknowthattheOdum(1971)*ThispaperissponsoredbyNationalScienceFundation… 相似文献
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V. S. Sergeev 《Journal of Applied Mathematics and Mechanics》2002,66(6):1376-932
Systems with aftereffect are considered. The state of these systems is described by integrodifferential equations of the Volterra type, which depend on functionals in integral form and, in particular, on analytic functionals which are represented by Frechet series. The integral kernels can allow of singularities of Abel kernel singularities. The total stability (i.e. stability under persistent disturbances) is investigated, and the structure of the general solution is investigated in the neighbourhood of zero for an equation with a holomorphic non-linearity assuming asymptotic stability of the trivial solution of the linearized unperturbed equation. The conditions for instability are given in the critical case of a single zero root, which generalise results obtained previously. 相似文献