CRITICAL POINTS RESULT FOR THE C1,1 FUNCTIONAL AND THE RELATIVE CATEGORY THEORY

Abstract

We show the existence of at least four nontrivial critical points of the C 1,1 functional f on the Hilbert space H = X0 ⊕ X1 ⊕ X2 ⊕ X3 ⊕ X4, Xi, i = 0, 1, 2, 3 are finite dimensional, with f (0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies (P.S.)c condition, and f |X0⊕X4 has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

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