中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/19/12/120201

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Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

黄俊杰1, 阿拉坦仓1, 王华2   

  1. (1)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; (2)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
  • 收稿日期:2010-01-27 修回日期:2010-03-15 出版日期:2010-12-15 发布日期:2010-12-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10962004 and 11061019), the Doctoral Foundation of Inner Mongolia (Grant Nos. 2009BS0101 and 2010MS0110), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070126002), and the Chunhui Program of the Ministry of Education of China (Grant No. Z2009-1-01010).

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

Huang Jun-Jie(黄俊杰)a),Alatancang(阿拉坦仓)a), and Wang Hua(王华)a)b)†   

  1. a School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; b Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
  • Received:2010-01-27 Revised:2010-03-15 Online:2010-12-15 Published:2010-12-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10962004 and 11061019), the Doctoral Foundation of Inner Mongolia (Grant Nos. 2009BS0101 and 2010MS0110), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070126002), and the Chunhui Program of the Ministry of Education of China (Grant No. Z2009-1-01010).

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摘要： This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Abstract: This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Key words: off-diagonal operator matrix, completeness, double eigenfunction expansion method, elasticity theory

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