Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 652-661.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 34B20
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