Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1534-1541.

• Articles • Previous Articles     Next Articles

Limit-point and Limit-circle Classification of |Singular Sturm-Liouville Equations with Complex Coefficients

 JING Hai-Bin1, QI Jian-Gang2, YUE Chong-Shan3   

  1. 1.Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering, Hebei Zhangjiakou 075000;
    2.Faculty of Mathematics and Statistics, Shandong University at Weihai, Shandong Weihai 264209;
    3.Department of Mathematics, Hebei North University, Hebei Zhangjiakou 075000
  • Received:2008-12-17 Revised:2010-01-06 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    山东省自然科学基金(Y2008A02)资助

Abstract:

By using limit-point(circle) classification theory of symmetric Hamiltonian differential systems, different from the method used by B.M.Brown et al, the paper gives the Sims classification of singular Sturm-Liouville equations with complex coefficients: limit-point-1 case, limit-point-2 case and limit-circle case. Then two limit-point-1 case criteria are obtained. Furthermore, the authors give an affirmative answer to the open problem of B.M.Brown et al by an example.

Key words: Singular Sturm-Liouville equations, Limit-point case, Complex coefficients

CLC Number: 

  • 34B24
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