# An index theory with applications to homoclinic Orbits of Hamiltonian systems and Dirac equations

10 Feb 2018 Wang Qi Liu Chungen

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

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• FUNCTIONAL ANALYSIS