中文摘要：

本文研究对边滑支边界条件的矩形板方程的无穷维Hamilton算子本征函数系，证明该无穷维Hamilton算子广义本征函数系在Cauchy主值意义下的完备性．进而推导出原矩形板方程的一般解，并对该平面弹性问题指出什么样的边界条件可按此方法求解．最后应用具体的算例说明所得结论的合理性．

英文摘要：

The eigenfunction system of the infinite dimensional Hamiltonian operator appearing in the rectangular plates with two opposite edges slidingly supported is studied. In the sense of Cauchy＇s principal value, the completeness of the extended eigenfunction system is proved. Then the general solutions for the rectangular plates is derived. Furthermore, it is indicated under what boundary conditions the plane elasticity problem can be solved by this method. Finally, the validity of the results is verified by a specific example.