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

In this paper, we will define the index pair $$(i_A(B),\nu _A(B))$$ ( i A ( B ) , ν A ( B ) ) by the dual variational method, and… Click to show full abstract

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

Keywords: dirac equations; index; homoclinic orbits; index theory; equations index; hamiltonian systems

Journal Title: Journal of Dynamics and Differential Equations
Year Published: 2018

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