RESONANT FORCED OSCILLATIONS IN SYSTEMS WITH PERIODIC NONLINEARITIES

被引：1
|
作者：
Krasnosel'skii, Alexander [1 ]
机构：
[1] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 01期
关键词：
Forced periodic oscillations; higher order ODE; resonance; unbounded set of solutions; periodic nonlinearities; method of stationary phase; EQUATIONS;
D O I：
10.3934/dcds.2013.33.239
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present an approach to study degenerate ODE with periodic nonlinearities; for resonant higher order nonlinear equations L (p) x = f (x) + b (t); p = d/dt with 2 pi-periodic forcing b and periodic f we give multiplicity results, in particular, conditions of existence of infinite and unbounded sets of 2 pi-periodic solutions.
引用
收藏
页码：239 / 254
页数：16
相关论文
共 50 条
  • [41] Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension
    Gentile, Guido
    Mazzoccoli, Alessandro
    Vaia, Faenia
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2019, 21 (07)
  • [42] NEW THEOREMS ON FORCED PERIODIC OSCILLATIONS IN NON-LINEAR CONTROL SYSTEMS.
    Krasnosel'skii, A.M.
    Journal of Applied Mathematics and Mechanics, 1986, 50 (02): : 165 - 170
  • [43] Periodic solutions to differential systems with unbounded or periodic nonlinearities
    Feng, Jian-Xia
    Han, Zhi-Qing
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) : 1264 - 1278
  • [44] Volterra Equations with Periodic Nonlinearities: Multistability, Oscillations and Cycle Slipping
    Smirnova, Vera B.
    Proskurnikov, Anton, V
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (05):
  • [45] SENSITIVITY OF A TURBULENT FLAME TO FORCED PERIODIC SONIC OSCILLATIONS
    SKLYAROV, VA
    FURLETOV, VI
    COMBUSTION EXPLOSION AND SHOCK WAVES, 1986, 22 (06) : 689 - 694
  • [46] Electromechanical Mode Estimation in the Presence of Periodic Forced Oscillations
    Agrawal, Urmila
    Follum, Jim
    Pierre, John W.
    Duan, Dongliang
    IEEE TRANSACTIONS ON POWER SYSTEMS, 2019, 34 (02) : 1579 - 1588
  • [47] Branches of Forced Oscillations Induced by a Delayed Periodic Force
    Calamai, Alessandro
    Pera, Maria Patrizia
    Spadini, Marco
    ADVANCED NONLINEAR STUDIES, 2019, 19 (01) : 149 - 163
  • [48] Electromechanical Mode Estimation in the Presence of Periodic Forced Oscillations
    Agrawal, Urmila
    Follum, Jim
    Pierre, John
    Duan, Dongliang
    2021 IEEE POWER & ENERGY SOCIETY GENERAL MEETING (PESGM), 2021,
  • [49] Periodic oscillations of forced pendulums with very small length
    Fonda, A
    Zanolin, F
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 : 67 - 76
  • [50] PERIODIC OSCILLATIONS OF FORCED PENDULUM-LIKE EQUATIONS
    MAWHIN, J
    LECTURE NOTES IN MATHEMATICS, 1982, 964 : 458 - 476
12345