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.
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.
基金
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)
the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
