A Lusternik-Schnirelmann Type Theorem for C1-Frechet Manifolds

Jump To References Section


  • ,UA
  • ,UA




Lusternik-Schnirelmann Theorem, Frechet Finsler Manifolds, Deformation Lemma
58E05, 58E30


We prove a Lusternik-Schnirelmann type theorem for a C1- function φ : M → R, where M is a connected infinite dimensional Frechet manifold of class C1. To this end, in this context we prove the so-called Deformation Lemma and by using it we derive the result generalizing the Minimax Principle.


Download data is not yet available.


Metrics Loading ...



How to Cite

Eftekharinasab, K., & Lastivka, I. (2021). A Lusternik-Schnirelmann Type Theorem for C<sup>1</sup>-Frechet Manifolds. The Journal of the Indian Mathematical Society, 88(3-4), 309–322. https://doi.org/10.18311/jims/2021/27836
Received 2021-05-19
Accepted 2021-05-19
Published 2021-06-14



F. E. Browder, Nonlinear Eigenvalue Problems and Group Invariance, In: Browder F. E. (eds) Functional Analysis and Related Fields (1970), 1 - 58.

N. Ghoussoub, A Min-Max principle with a relaxed boundary condition, Proc. Amer. Math. Soc., 117 (2)(1993), 439 - 447.

J. Milnor, Morse theory, Princeton University Press, 1963.

K-H. Neeb, Towards a Lie theory for locally convex groups, Japanese. J. Math., 1 (2006), 291 - 468.

K-H. Neeb, Borel-Weil theory for loop groups, In: Huckleberry A., Wurzbacher T. (eds) In nite dimensional Kahler manifolds. DMV Seminar Band, 31 (2001), 179 - 229.

R. Palais, Lusternik-Schnirelman theory on Banach manifolds, Topology, 5 (2) (1966), 115 - 132.

R. Palais, Morse theory on Hilbert manifolds, Topology, 2 (4)(1966), 299 - 340.

R. Palais, The Morse lemma for Banach spaces, Bull. Amer. Math. Soc., 75 (5) (1969), 968 - 972.

R. Palais, Foundations of Global Non-Linear Analysis, Watham, Mass.: Dept. of Mathematics, Brandeis University, 1966.

A. Szulkin, Ljusternik-Schnirelmann theory on C1-manifolds, Annales de l'I. H. P., section C, 5 (2)(1988), 119 - 139

R. S. Sadyrkhanov, On in nite dimensional features of proper and closed mappings, Proc. Amer. Math. Soc., 98 (4)(1986), 643 - 648.

S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. Math., 80 (2)(1964), 382 - 396.

T. N. Subramaniam, Slices for the actions of smooth tame Lie groups, PhD thesis, Brandeis University, 1984.

A. J. Tromba, A general approach to Morse theory, J. Di er. Geom., 12 (1)(1977), 47 - 85.

K. Uhlenbeck, Morse theory on Banach manifolds, J. Funct. Anal, 10 (4)(1972), 430 - 445.