Relative index theories and applications
Keywords
Hamiltonian system, symplectic path, Maslov P-index, relative index, minimal periodic problemAbstract
We develop some relative index theories for abstract operator equations. As applications, we prove a new Galerkin approximation formula and a new saddle point reduction formula for the $P$-index. We apply these new formulas to the minimal periodic problem for $P$-symmetric periodic solutions of nonlinear Hamiltonian systems.References
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