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Journal of Convex Analysis 22 (2015), No. 4, 1107--1124
Copyright Heldermann Verlag 2015



Critical Points on Closed Convex Sets vs. Critical Points and Applications

Salvatore A. Marano
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy
marano@dmi.unict.it

Sunra J. N. Mosconi
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy
mosconi@dmi.unict.it



The existence of multiple critical points for a locally Lipschitz continuous functional Φ on a closed convex subset C of a Banach space X is investigated. The problem of finding extra conditions under which critical points for Φ on C turn out to be critical on X is also addressed. Two applications concerning elliptic variational-hemivariational inequalities are then worked out.

Keywords: Multiple critical points, functional defined on closed convex set, Schauder invariance condition, elliptic variational-hemivariational inequality.

MSC: 58E05; 49J40; 49J52

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