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

Salvatore A. Marano; Sunra J. N. Mosconi

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Salvatore A. Marano

Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

marano@dmi.unict.it

Sunra J. N. Mosconi

Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

mosconi@dmi.unict.it

Keywords

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

Mathematics Subject Classification

58E05; 49J40; 49J52

Suggested citation

S. A. Marano, S. J. N. Mosconi. “Critical Points on Closed Convex Sets vs. Critical Points and Applications.” Journal of Convex Analysis 22 (2015), No. 4, 1107–1124.