2025年4月4日 19:00 星期五
首页 > 过刊浏览>2013年第5卷第1期 >81-85
PDF HTML阅读 XML下载 导出引用 引用提醒
二阶奇异动力系统的非平凡周期解
作者:
基金项目:

国家自然科学基金(11171090)


Nontrivial periodic solutions for second order singular dynamical systems
Author:
  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献
    • | | | |
  • 文章评论
    摘要:

    应用Leray-Schauder非线性二择一原理研究二阶动力系统x+k2x=f(t,x)+e(t)非平凡周期解的存在性,其中0<k<π/T,f∈C((R/TZ)×RN\{0},RN)在原点具有排斥的奇性.不需要任何的强制性条件,既可以处理强奇性,也可以处理弱奇性.

    Abstract:

    In this paper,we study the existence of nontrivial periodic solutions for second order dynamical systems x+k2x=f(t,x)+e(t), here 0<k<π/T and f∈C((R/TZ)×RN\{0},RN) has a repulsive singularity at the origin.We do not need any coercivity conditions,therefore we can deal with the case of a strong singularity as well as the case of a weak singularity.The proof is based on a nonlinear alternative principle of Leray-Schauder.

    参考文献
    [1] Chu J F,Torres P J,Zhang M R.Periodic solutions of second order non-autonomous singular dynamical systems[J].Journal of Differential Equations,2007,239(1):196-212
    [2] Habets P,Sanchez L.Periodic solution of some Lienard equations with singularities[J].Proceedings of the American Mathematical Society,1990,109(4):1135-1144
    [3] Lazer A C,Solimini S.On periodic solutions of nonlinear differential equations with singularities[J].Proceedings of the American Mathematical Society,1987,99(1):109-114
    [4] Gordon W B.Conservative dynamical systems involving strong forces[J].Transactions of the American Mathematical Society,1975,204:113-135
    [5] Chu J F,Torres P J.Applications of Schauder's fixed point theorem to singular differential equations[J].Bulletin of the London Mathematical Society,2007,39(4):653-660
    [6] Jiang D Q,Chu J F,Zhang M R.Multiplicity of positive periodic solutions to superlinear repulsive singular equations[J].Journal of Differential Equations,2005,211(2):282-302
    [7] Rachunkov I,Tvrdy M,Vrkoc I.Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems[J].Journal of Differential Equations,2001,176(2):445-469
    [8] Torres P J.Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem[J].Journal of Differential Equations,2003,190(2):643-662
    [9] Franco D,Webb J R L.Collisionless orbits of singular and nonsingular dynamical systems[J].Discrete and Continuous Dynamical System,2006,15(3):747-757
    [10] O'Regan D.Existence theory for nonlinear ordinary differential equations[M].Dordrecht:Kluwer Academic Publishers,1997
    相似文献
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

廖芳芳,许晓婕.二阶奇异动力系统的非平凡周期解[J].南京信息工程大学学报(自然科学版),2013,5(1):81-85
LIAO Fangfang, XU Xiaojie. Nontrivial periodic solutions for second order singular dynamical systems[J]. Journal of Nanjing University of Information Science & Technology, 2013,5(1):81-85

复制
分享
文章指标
  • 点击次数:1100
  • 下载次数: 2549
  • HTML阅读次数: 0
  • 引用次数: 0
历史
  • 收稿日期:2012-04-16

地址：江苏省南京市宁六路219号    邮编：210044

联系电话：025-58731025    E-mail：nxdxb@nuist.edu.cn

南京信息工程大学学报 ® 2025 版权所有  技术支持：北京勤云科技发展有限公司