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An index theory with applications to homoclinic orbits of Hamiltonian systems and Dirac equations. (English) Zbl 1446.49028

The existence and multiplicity of homoclinic orbits of nonlinear Hamiltonian systems and solutions of nonlinear Dirac equations are investigated by introducing an index pair by the dual variational method.

MSC:

49N15 Duality theory (optimization)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
47J30 Variational methods involving nonlinear operators
47A75 Eigenvalue problems for linear operators
37J51 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods
35Q41 Time-dependent Schrödinger equations and Dirac equations
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References:

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