A Lusternik-Schnirelmann Type Theorem for C1-Frechet Manifolds


Affiliations

  • Institute of Mathematics of NAS of Ukraine, Topology Lab, Kyiv, Ukraine
  • National Aviation University, Higher Mathematics Department, Kyiv, Ukraine

Abstract

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.

Keywords

Lusternik-Schnirelmann Theorem, Frechet Finsler Manifolds, Deformation Lemma

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