Branches of forced oscillations in degenerate systems of second-order ODEs

被引：3
|
作者：
Lewicka, Marta [2 ]
Spadini, Marco [1 ]
机构：
[1] Univ Florence, Dipartimento Matemat Applicata, I-50139 Florence, Italy
[2] Univ Minnesota, Minneapolis, MN 55455 USA
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 09期
关键词：
coupled differential equations; branches of periodic solutions; fixed point index;
D O I：
10.1016/j.na.2007.02.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We use fixed point index methods to Study the set of forced oscillations in periodically perturbed systems of ODEs on manifolds. We prove the existence of branches of periodic solutions for a particular class of system where, contrary to the usual 'nondegeneracy' assumption, the leading vector field is neither trivial nor has a set of compact zeros. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2623 / 2628
页数：6
相关论文
共 50 条
  • [21] Second-order operators with degenerate coefficients
    Ter Elst, A. F. M.
    Robinson, Derek W.
    Sikora, Adam
    Zhu, Yueping
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2007, 95 : 299 - 328
  • [22] Computation of periodic solutions in perturbed second-order ODEs
    Navarro, Juan F.
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) : 171 - 177
  • [23] FORCED SECOND-ORDER NONLINEAR OSCILLATION
    TEUFEL, H
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A308 - A308
  • [24] The period function for second-order quadratic odes is monotone
    Gasull A.
    Guillamon A.
    Villadelprat J.
    Qualitative Theory of Dynamical Systems, 2004, 4 (2) : 329 - 352
  • [25] Multivalue-multistage Method for Second-order ODEs
    Ismail, Ainathon
    Rabiei, Faranak
    PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM24): MATHEMATICAL SCIENCES EXPLORATION FOR THE UNIVERSAL PRESERVATION, 2017, 1870
  • [26] FORCED SECOND-ORDER NONLINEAR OSCILLATION
    TEUFEL, H
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 40 (01) : 148 - &
  • [27] Taylor Series Method for Second-Order Polynomial ODEs
    Latypov, Viktor
    Sokolov, Sergei
    2015 INTERNATIONAL CONFERENCE "STABILITY AND CONTROL PROCESSES" IN MEMORY OF V.I. ZUBOV (SCP), 2015, : 62 - 64
  • [28] Adaptive finite elements for a set of second-order ODEs
    Urban, Jakub
    Preinhaelter, Josef
    JOURNAL OF PLASMA PHYSICS, 2006, 72 (06) : 1041 - 1044
  • [29] Point equivalence of second-order ODEs: Maximal invariant classification order
    Milson, Robert
    Valiquette, Francis
    JOURNAL OF SYMBOLIC COMPUTATION, 2015, 67 : 16 - 41
  • [30] Linearizing Systems of Second-Order ODEs via Symmetry Generators Spanning a Simple Subalgebra
    Campoamor-Stursberg, R.
    Gueron, J.
    ACTA APPLICANDAE MATHEMATICAE, 2013, 127 (01) : 105 - 115
12345