Eigenvalue problem of a class of fourth-order Hamiltonian operators  

作　　者：WANG Hua HUANG Jun-jie Alatancang 

机构地区：[1]College of Sciences, Inner Mongolia University of Technology [2]School of Mathematical Sciences, Inner Mongolia University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2013年第1期101-115,共15页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (11261034,11061019);the Chunhui Program of Ministry of Education of China (Z2009-1-01010);the Inner Mongolia Natural Science Foundation of China (2010MS0110)

摘　　要：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.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.

关 键 词：Hamiltonian operator EIGENVALUE MULTIPLICITY completeness. 

分 类 号：O177[理学—数学]