数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 652-661.

• 论文 • 上一篇    下一篇

奇异哈密顿微分系统的粘结引理和亏指数

杨杰1, 綦建刚2, 景海斌3   

  1. 1.山东师范大学数学科学学院 济南 250014|2.山东大学威海分校数学与统计学院 山东 威海 264209|3.河北建筑工程学院数理系 |河北 张家口 075024
  • 收稿日期:2008-12-19 修回日期:2010-04-07 出版日期:2011-06-25 发布日期:2011-06-25
  • 基金资助:

    山东省自然科学基金(Y2008A02)资助

Patching Lemma and Deficiency Indices for |Singular Hamiltonian Differential Systems

 YANG Jie1, QI Jian-Gang2, JING Hai-Bin3   

  1. 1.Department of Mathematics, Shandong Normal University, Jinan 250014|2.Department of |Mathematics, Shandong University at Weihai, Shandong Weihai 264209|3.Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering,
    Hebei Zhangjiakou 075024
  • Received:2008-12-19 Revised:2010-04-07 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    山东省自然科学基金(Y2008A02)资助

摘要:

建立了奇异哈密顿微分系统的``粘结"引理, 这是H.D.Niessen 和A., Zettl关于二阶微分方程相应结果的推广. 同时也得到了Rellich和Rosenberger关于二阶微分方程非振动结果在奇异哈密顿微分系统上的推广形式, 并由此建立了奇异哈密顿微分系统极限点型判断准则.该结果不但推广了綦、陈的相应结果, 包含了S.L.Clark 和 F.Gesztesy 的结果, 同时也得到了奇异哈密顿微分系统的Hartman 型极限点型判断准则.

关键词: 哈密顿微分系统, 振动性, 亏指数, 极限点型

Abstract:

The "patching" lemma for singular Hamiltonian differential systems is obtained, which is the extension version of the corresponding result of H.D. Niessen and A. Zettl for second order differential equations. With applications, the non-oscillation criterion of Rellich and Rosenberger  type is generalized to singular Hamiltonian differential systems and the limit-point criteria of J. Qi and Sh. Chen, S.L. Clark and F. Gesztesy are improved.

Key words: Hamiltonian differential system, Oscillation, Deficiency index, Limit-point case

中图分类号: 

  • 34B20