On critical point theory for indefinite functionals in the presence of symmetries

作者：Vieri Benci · 发表于：Transactions of the American Mathematical Society · 年份：1982 · DOI：10.1090/s0002-9947-1982-0675067-x · 被引用次数：303 · 研究领域：Nonlinear Differential Equations Analysis、Nonlinear Partial Differential Equations、Advanced Differential Equations and Dynamical Systems

We consider functionals which are not bounded from above or from below even modulo compact perturbations, and which exhibit certain symmetries with respect to the action of a compact Lie group. We develop a method which permits us to prove the existence of multiple critical points for such functionals. The proofs are carried out directly in an infinite dimensional Hilbert space, and they are based on minimax arguments. The applications given here are to Hamiltonian systems of ordinary differential equations where the existence of multiple time-periodic solutions is established for several classes of Hamiltonians. Symmetry properties of these Hamiltonians such as time translation invariancy or evenness are exploited.