REMARKS ON PERIODIC RESONANT PROBLEMS WITH NONLINEAR DISSIPATION

被引：0
|
作者：
Sanchez, Luis [1 ]
Silva, Joao G. [2 ]
机构：
[1] Univ Lisbon, Fac Ciencias, CMAFcIO, P-1749016 Lisbon, Portugal
[2] Univ Lisbon, Fac Ciencias, P-1749016 Lisbon, Portugal
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年
关键词：
Periodic solution; resonance; bounded solution; THEOREM;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the periodic problem for a 2nd order ODE with non-invertible linear part, and mild nonlinear dissipation term. The motivation for this study is a paper by Lazer [9]. We add a bounded restoring force g(u) and show that the sufficient condition (of Landesman-Lazer type) given in [9] still implies the existence of a periodic solution in our case. We also comment on some variants of the problem and on the existence of bounded solutions.
引用
收藏
页码：203 / 212
页数：10
相关论文
共 50 条
  • [21] Remarks on the Periodic Conformable Sturm-Liouville Problems
    Wang, Wei-Chuan
    COMPLEXITY, 2023, 2023
  • [22] Global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation
    Nakao, M
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 190 (01) : 81 - 107
  • [23] Remarks on nonlinear elliptic problems on long domains
    Dancer, EN
    ADVANCED NONLINEAR STUDIES, 2005, 5 (02) : 253 - 263
  • [24] Periodic waves and solitons in a nonlinear fibre with resonant impurities
    Cavalcanti, SB
    Kamchatnov, AM
    Kraenkel, RA
    Umarov, BA
    JOURNAL OF MODERN OPTICS, 2002, 49 (13) : 2183 - 2193
  • [25] Multiple Solutions for Nonlinear Periodic Problems
    Kyritsi, Sophia Th.
    Papageorgiou, Nikolaos S.
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2013, 56 (02): : 366 - 377
  • [26] Positive solutions for nonlinear periodic problems
    Michael E. Filippakis
    Nikolaos S. Papageorgiou
    Vasile Staicu
    Positivity, 2008, 12 : 733 - 750
  • [27] Positive solutions for nonlinear periodic problems
    Filippakis, Michael E.
    Papageorgiou, Nikolaos S.
    Staicu, Vasile
    POSITIVITY, 2008, 12 (04) : 733 - 750
  • [28] Periodic problems and problems with discontinuities for nonlinear parabolic equations
    Tiziana Cardinali
    Nikolaos S. Papageorgiou
    Czechoslovak Mathematical Journal, 2000, 50 : 467 - 497
  • [29] Periodic problems and problems with discontinuities for nonlinear parabolic equations
    Cardinali, T
    Papageorgiou, NS
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2000, 50 (03) : 467 - 497
  • [30] Multiple Nontrivial Solutions for Doubly Resonant Periodic Problems
    Papageorgiou, Nikolaos S.
    Staicu, Vasile
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2010, 53 (02): : 347 - 359
12345