On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations  

作　　者：额布日力吐 阿拉坦仓 

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

出　　处：《Communications in Theoretical Physics》2010年第3期569-574,共6页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No. 10962004;the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002

摘　　要：The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy＇s principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.

关 键 词：plate bending equation infinite-dimensioanl Hamiltonian operator eigenfunction system COMPLETENESS general solution 

分 类 号：O177[理学—数学]