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一类非自治二阶系统的多重周期解 被引量：6

Multiplicity of periodic solution of a class of non-automous second order system
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摘要 利用广义鞍点定理研究非自治二阶系统周期解的存在性。在具有部分周期位势和线性增长非线性项时,给出了相关多重周期解存在的充分条件,所得结论推广了已知结果。 In this paper,we investigate the existence of periodic solution for non-autonmous second order systems with partially periodic potential or linear nonlinearity by the general saddle point theorem.Some sufficient conditions for the existence of multiple periodic solutions are obtained,and these results improve existing ones.
作者 张申贵
机构地区 西北民族大学数学与计算机科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2011年第11期64-69,共6页 Journal of Shandong University(Natural Science)
基金 国家民委科研资助项目(05XB07)
关键词 二阶系统 线性增长非线性项 部分周期 周期解 临界点 second order system linear nonlinearity partially periodic periodic solution critical point
分类号 O175.12 [理学—基础数学]
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参考文献6

  • 1RABINOWITZ P H. On a class of functionals invariant under a Z^n action [J]. Trans Amer Math Soc, 1988, 310:303-311.
  • 2CHANG K C. On the periodic nonlinearity and multiplicity of solutions [J]. Nonlinear Analysis TMA, 1989, 13:527-537.
  • 3WU Xingping. Periodic solution of nonautomous second order system with bounded nonlinearity[J]. J Math Anal Appl, 1999, 230:135-141.
  • 4TANG Chunlei. A note on periodic solutions of second order systems [ J]. Proc Amer Math Soc, 2003, 132:1295-1393.
  • 5LIU Jiaquan. A generalized saddle point theorem [J]. J Diff Equat, 1989,82:372-385.
  • 6MAWHIN J, WILLEM M. Critical point theory and Hamiltonian systems[M ]. NewYork: Springer-Verlag, 1989.

同被引文献36

  • 1Berger M S, Schechter M. On the solvability of semilinear gradient operator equations [ J ]. Adv Math, 1977,25 (2) : 97-132.
  • 2Mawhin J, Willem M. Critical point theory and Hamihonian systems [ M ]. Berlin, New York : Springer-Verlag, 1989.
  • 3Tang Chunlei. Periodic solutions for nonautonomous second order systems with sublinear nonlinearity [ J ]. Proc Amer Math Soc, 1998,126 ( 11 ) :3263-3270.
  • 4Wu Xingping, Tang Chunlei. Periodic solutions of a class of non-autonomous second-order systems [ J ]. J Math Anal Appl, 1999,236 (2) : 227 -235.
  • 5Ma Jian,Tang Chunlei. Periodic solutions for some nonau- tonomous second-order systems [ J ]. J Math Anal Appl, 2002,275 ( 2 ) :482-494.
  • 6Tang Chunlei. Periodic solutions of non-autonomous sec- ond-order systems with y-quasisubadditive potential [ J ]. J Math Anal Appl, 1995,189 (3) :671-675.
  • 7Tang Chunlei. Periodic solutions of non-autonomous second order systems [ J ]. J Math Anal Appl, 1996,202 (2) :465- 469.
  • 8Tang Chunlei, Wu Xingping. Periodic solutions for second order systems with not uniformly coercive potential [ J ]. J Math Anal Appl,2001,259(2) :386-397.
  • 9Mawhin J. Semi-coercive monotone variational problems [J]. Acad Roy Belg Bull C1 Sei,1987,73(5) :118-130.
  • 10Tang Chunlei, Wu Xingping. Periodic solutions for a class of non-autonomous subquadratic second order Hamihonian systems [ J ]. J Math Anal Appl, 2002,275 (2) : 870-882.

引证文献6

二级引证文献8

山东大学学报（理学版）
2011年 第11期

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