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Critical points on closed convex sets vs. critical points and applications. (English) Zbl 1334.49052

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

MSC:

49J52 Nonsmooth analysis
49J40 Variational inequalities
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