Algebraic Index Of Zero Eigenvalues For Two Kinds Of Infinite-dimensional Hamiltonian Operators

For the general form of infinite-dimensional Hamiltonian operators,the algebraic index of zero eigenvalue of the operators is studied.Making the best of the structural characteristics of infinite-dimensional Hamiltonian operators,some sufficient conditions are obtained for the algebraic index of two kinds of the operators to be 1 or 2,respectively.The first chapter introduces the basic definitions and lemmas required in the following proofs and it outlines the background and significance of the research.The second chapter dis-cusses the algebraic index of zero eigenvalues of a class of 2 × 2 infinite-dimensional Hamiltonian operators.The sufficient conditions for the algebraic index to be 1 and the algebraic index to be 2 are obtained.In the third chapter,we study the algebraic index of zero eigenvalues of a class of 4 × 4 infinite-dimensional Hamiltonian operators arising from the symplectic elasticity problems.And the obtained results are applied to some concrete mechanical models.