  Over the past few years, it is gradually understood that de Rham Cohomology
Theory is closely related to Saint-Venant's compatibility condition in the
Elasticity Theory. In this article, we will discuss the Hodge Theory and de
Rham Cohomology Theory hidden in the Lame Equation and in the Plate Theory. we
will prove a Decomposition Theorem for the solutions of the Lame Equation, and
then use this Decomposition Theorem to present a modified Plate Theory, which
is compatible with the general principles of Physics and the mathematical
structure of the Lame Equation.
