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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On critical point theory for indefinite functionals in the presence of symmetries
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by Vieri Benci PDF
Trans. Amer. Math. Soc. 274 (1982), 533-572 Request permission

Abstract:

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.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 274 (1982), 533-572
  • MSC: Primary 58E05; Secondary 58F22, 70H05
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0675067-X
  • MathSciNet review: 675067