Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action functionals obtained by a generalization of Bogomolnyi’s trick of ‘completing squares’. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
GHOUSSOUB Nassif
. Hamiltonian systems as selfdual equations[J]. Frontiers of Mathematics in China, 2008
, 3(2)
: 167
-193
.
DOI: 10.1007/s11464-008-0021-1
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