共查询到20条相似文献,搜索用时 15 毫秒
1.
Anatoli F. Ivanov Bernhard Lani-Wayda 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(2):205-233
We derive sufficient conditions for the stability and instability of periodic solutions
of Kaplan–Yorke type to the equation
where f is even in the first and odd in the second argument. The criteria are based on the monotonicity of the coefficient in a transformed
version of the variational equation. For the special case of cubic f, we show that this monotonicity property is satisfied if and only if the set
is contained in a region E defined by a quadratic form (bounded by an an ellipse or a hyperbola). The coefficients of this quadratic form are expressible
in terms of the Taylor coefficients of f. Further, the parameter α in the equation and the amplitude z of the periodic solution are related by an elliptic integral. Using the relation between this integral and the arithmeticgeometric
mean, we obtain upper and lower estimates on this relation, and on the inverse function. Combining these estimates with the
inequality that defines the region E, we obtain stability criteria explicit in terms of the Taylor coefficients of f. These criteria go well beyond local stability analysis, as examples show.
This research was supported by the Alexander von Humboldt Foundation (Germany)
Received: March 14, 2005; revised: August 16, 2005 相似文献
2.
A new mixed formulation for elasticity 总被引:7,自引:0,他引:7
Summary We propose a new mixed variational formulation for the equations of linear elasticity. It does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.Dedicated to Professor Ivo Babuka on the occasion of his sixtieth birthdaySupported by NSF Grant DMS-8313247Supported by NSF Grant DMS-8402616 相似文献
3.
András Bátkai 《Integral Equations and Operator Theory》2002,44(4):383-396
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.The author thanks W. Desch (Graz), I. Gyri (Veszprém) and R. Schnaubelt (Halle) for helpful discussions. 相似文献
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Timothy J. Healey 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(5):809-816
We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish orbitai stability (modulo this collection of relative equilibria). For a well-defined class of soft materials, there is an upper bound on the axial speed sufficient for stability; stiff materials are shown to be orbitally stable at any axial speed. 相似文献
6.
Wolfgang M. Ruess 《Journal of Evolution Equations》2003,3(2):361-373
We present a general principle of linearized stability at an equilibrium point for the Cauchy problem , for an -accretive, possibly multivalued, operator in a Banach space , that has a linear 'resolvent-derivative' . The result is applied to derive linearized stability results for the case of under 'minimal' differentiability assumptions on the operators and at the equilibrium point, as well as for partial differential delay equations.
RID="h1"
ID="h1"To the memory of Philippe Bénilan 相似文献
7.
Summary This paper continues earlier work by the same authors concerning the shape and size of the stability regions of general linear discretization methods for initial value problems. Here the treatment is extended to cover also implicit schemes, and by placing the accuracy of the schemes into a more central position in the discussion general method-free statements are again obtained. More specialized results are additionally given for linear multistep methods and for the Taylor series method.This research has been supported by Swiss National Foundation, Grant No. 82-524.077This research has been supported by the Heinrich-Hertz-Stiftung, B 32 No. 203/79 相似文献
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LetX be a Banach space and 1p<. LetL be a bounded linear operator fromL
p
([–1,0],X) intoX. Consider the delay differential equationu(t)=Lu
t
,u(0)=x,u
0=f on the state spaceL
p
([–1,0],X). We prove that a mild solutionu(t)=u(t;x,f) is a small solution if and only if the Laplace transform ofu(t;x,f) extends to an entire function. The same result holds for the state spaceC([–1,0],X).This paper was written while the authors were affiliated with the University of Tübingen. It is part of a research project supported by the Deutsche Forschungsgemeinschaft DFG. The authors warmly thank Professor Rainer Nagel and the AG Funktionalanalysis for the stimulating and enjoyable working environment.Support by DAAD is gratefully acknowledged.Support by an Individual Fellowship from the Human Capital and Mobility programme of the European Community is gratefully acknowledged. 相似文献
11.
Ioan I. Vrabie 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7047-7060
In this paper, we prove a sufficient condition for the global existence of bounded C0-solutions for a class of nonlinear functional differential evolution equation of the form where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, is a nonempty, convex, weakly compact valued, and almost strongly–weakly u.s.c. multi-function, and is nonexpansive. 相似文献
12.
This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice . For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented. 相似文献
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Summary In the paper conditions for the existence ofL
p-conditions (1 p ) of linear impulsive equations in a Banach space are found. 相似文献
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Sufficient conditions of the permanence and global stability for the general delayed ratio-dependent predator-prey model
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The state-dependent delay differential equation
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Differential inclusions of a retarded type with a small real parameter >0 in part of the derivatives are considered. We prove upper semicontinuity of the map set of solutions at =0+ inC[0, 1]×(L
2(0, 1)–weak) topology. In case of constant delay lower semicontinuity inC[0, 1]×(L
1(0, 1)–strong) is shown. 相似文献
18.
Summary The paper concerns solution manifolds of nonlinear parameterdependent equations (1)F(u, )=y0 involving a Fredholm operatorF between (infinite-dimensional) Banach spacesX=Z× andY, and a finitedimensional parameter space . Differntial-geometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of , estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundaryvalue problems for partial differential equations.This work was in part supported by the U.S. Air Force Office of Scientific Research under Grant 80-0176, the National Science Foundation under Grant MCS-78-05299, and the Office of Naval Research under Contract N-00014-80-C-0455 相似文献
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The paper considers the equationwhere the operator-valued bounded functions aj and bj are 2π-periodic, and the operator-valued kernels m and n are 2π-periodic with respect to the first argument. The connection between the input-output stability of the equation and the invertibility of a family of operators acting on the space of periodic functions is investigated. 相似文献