On The Algebraic Index Of The Zero Eigenvalue For Three Kinds Of Infinite-dimensional Hamiltonian Operators And Its Applications

According to the theory of symplectic elasticity,all Saint-Venant solutions of an e-lastic problems can be obtained directly via the zero eigenvalue solutions and the Jordan eigenfunction solutions of the derived infinite-dimensional Hamiltonian operators.The number of the zero eigenvalue solutions and the length of Jordan chain determine the zero algebraic index.For three kinds of the infinite-dimensional Hamiltonian operators arising from the symplectic elasticity,its geometric multiplicity and algebraic index are studied in this thesis.Moreover,the theoretical results have been applied into elasticity.Then,we analyze the physical meanings and form of the Saint-Venant solutions for the plane elasticity problems,the plate bending problems and the Stokes flow problems.