LIMIT RELATIVE CATEGORY THEORY APPLIED TO THE CRITICAL POINT THEORY

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 2, 2009, pp.311-319
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.2.311

Title & Authors

LIMIT RELATIVE CATEGORY THEORY APPLIED TO THE CRITICAL POINT THEORY

Jung, Tack-Sun; Choi, Q-Heung;

Jung, Tack-Sun; Choi, Q-Heung;

Abstract

Let H be a Hilbert space which is the direct sum of five closed subspaces and with of finite dimension. Let J be a functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies condition and has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

Keywords

functional;nonsmooth version classical deformation lemma;limit relative category theory;critical point theory;manifold with boundary; condition;

Language

English

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