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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Physical variational principles which satisfy the Palais-Smale condition


Author: William B. Gordon
Journal: Bull. Amer. Math. Soc. 78 (1972), 712-716
MSC (1970): Primary 70H25, 58F05; Secondary 58E99
MathSciNet review: 0299031
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  • 1. Melvyn S. Berger, On periodic solutions of second order Hamiltonian systems. I, J. Math. Anal. Appl. 29 (1970), 512–522. MR 0257470 (41 #2121)
  • 2. Melvyn S. Berger, Multiple solutions of nonlinear operator equations arising from the calculus of variations, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 10–27. MR 0270221 (42 #5112)
  • 3. Melvyn S. Berger, Periodic solutions of second order dynamical systems and isoperimetric variational problems, Amer. J. Math. 93 (1971), 1–10. MR 0276848 (43 #2588)
  • 4. William B. Gordon, On the relation between period and energy in periodic dynamical systems, J. Math. Mech. 19 (1969/1970), 111–114. MR 0245930 (39 #7236)
  • 5. William B. Gordon, A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential, J. Differential Equations 10 (1971), 324–335. MR 0292113 (45 #1200)
  • 6. William B. Gordon, Periodic solutions to Hamiltonian systems with infinitely deep potential wells, Ordinary differential equations (Proc. NRL-MRC Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971) Academic Press, New York, 1972, pp. 399–403. MR 0478224 (57 #17710)
  • 7. Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299–340. MR 0158410 (28 #1633)
  • 8. Richard S. Palais, Critical point theory and the minimax principle, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif, 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 185–212. MR 0264712 (41 #9303)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1972-12998-7
PII: S 0002-9904(1972)12998-7