An Index Theory with Applications to Homoclinic Orbits of Hamiltonian Systems and Dirac Equations

摘要

In this paper, we will define the index pair (i(A)(B), v(A)(B)) by the dual variational method, and show the relationship between the indices defined by different methods. As applications, we apply the index (i(A)(B), v(A)(B)) to study the existence and multiplicity of homoclinic orbits of nonlinear Hamiltonian systems and solutions of nonlinear Dirac equations.