Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory |
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| Authors: | Huang Jun-Jie Alatancang and Wang Hua |
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| Institution: | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China |
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| 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. |
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| Keywords: | off-diagonal operator matrix completeness double eigenfunction expansion method elasticity theory |
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