中文摘要：

对于一类Hamilton算子,考虑其特征值的重数,以及特征向量组和根向量组的完备性.首先给出了特征值的几何重数、代数指标和代数重数,再结合特征向量和根向量的辛正交性得到了特征向量组和根向量组完备的充分必要条件,最后将上述结果应用于板弯曲方程、平面弹性问题和Stokes流等问题中.

英文摘要：

In this paper, we consider the multiplicity of the eigenvalue and the completeness of the eigen and root vector system of a class of Hamiltonian operators. The geometric multiplicity, algebraic index and algebraic multiplicity of each eigenvalue is completely determined. Based on the above properties and the symplectic orthogonality of the associated eigen and root vectors, the necessary and sufficient condition for the eigen or root vector system to be complete is obtained. Moreover, the obtained results are tested for several problems, for example, the plate bending, plane elasticity, Stokes flow.