Proceedings of the Japan Academy, Series A, Mathematical Sciences

A Lusternik-Schnirelmann type theorem for locally Lipschitz functionals with applications to multivalued periodic problems

Vicenţiu D. Rǎdulescu

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 71, Number 7 (1995), 164-167.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195510608

Digital Object Identifier
doi:10.3792/pjaa.71.164

Mathematical Reviews number (MathSciNet)
MR1363906

Zentralblatt MATH identifier
0853.58031

Subjects
Primary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Secondary: 34C25: Periodic solutions

Citation

Rǎdulescu, Vicenţiu D. A Lusternik-Schnirelmann type theorem for locally Lipschitz functionals with applications to multivalued periodic problems. Proc. Japan Acad. Ser. A Math. Sci. 71 (1995), no. 7, 164--167. doi:10.3792/pjaa.71.164. https://projecteuclid.org/euclid.pja/1195510608


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References

  • [1] J A. Ambrosetti and P. H. Rabinowitz: Dual variational methods in critical point theory and applications. J. Funct. Anal., 14, 349-381 (1973).
  • [2] F. H. Clarke : Generalized gradients of Lipschitz functionals. Adv. in Math., 40, 52-67 (1981).
  • [3] F. H. Clarke : Generalized gradients and applications. Trans. Amer. Math. Soc., 205, 247-262 (1975).
  • [4] G. Lebourg: generalise. C (1975).
  • [5] L. Lusternik and L. Schnirelmann: Methodes Topologiques dans les Problemes Variationnels. Hermann, Paris (1934).
  • [6] J. Mawhin and M. Willem : Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations. J. Diff. Eq., 52, 264-287 (1984).
  • [7] R. Palais: Ljusternik-Schnirelmann theory on Banach manifolds. Topology, 5, 115-132 (1966).
  • [8] V. Radulescu: Mountain pass theorems for non-differentiable functions and applications. Proc. Japan Acad., 69A, 193-198 (1993).
  • [9] A. Szulkin : Critical point theory of Ljusternik-Schnirelmann type and applications to partial differential equations. Semin. Math. Sup., Presses Univ. Montreal (1989).