LIMIT RELATIVE CATEGORY THEORY APPLIED TO THE CRITICAL POINT THEORY

Title & Authors
LIMIT RELATIVE CATEGORY THEORY APPLIED TO THE CRITICAL POINT THEORY
Jung, Tack-Sun; Choi, Q-Heung;

Abstract
Let H be a Hilbert space which is the direct sum of five closed subspaces $\small{X_0,\;X_1,\;X_2,\;X_3}$ and $\small{X_4}$ with $\small{X_1,\;X_2,\;X_3}$ of finite dimension. Let J be a $\small{C^{1,1}}$ 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 $\small{(P.S.)^*_c}$ condition and $\small{f|X_0{\otimes}X_4}$ 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
$\small{C^{1,1}}$ functional;nonsmooth version classical deformation lemma;limit relative category theory;critical point theory;manifold with boundary;$\small{(P.S.)^*_c}$ condition;
Language
English
Cited by
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