Abstract
The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem.
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Supported by the National Natural Science Foundation of China (11261034,11061019), the Chunhui Program of Ministry of Education of China (Z2009-1-01010) and the Inner Mongolia Natural Science Foundation of China (2010MS0110).
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Wang, H., Huang, Jj. & Alatancang Eigenvalue problem of a class of fourth-order Hamiltonian operators. Appl. Math. J. Chin. Univ. 28, 101–115 (2013). https://doi.org/10.1007/s11766-013-3024-y
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DOI: https://doi.org/10.1007/s11766-013-3024-y