Details

Autor(en) / Beteiligte

• Bonanno, Gabriele

Titel

A critical point theorem via the Ekeland variational principle

Ist Teil von

• Nonlinear analysis, 2012-03, Vol.75 (5), p.2992-3007

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2012

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The aim of this paper is to establish the existence of a local minimum for a continuously Gâteaux differentiable function, possibly unbounded from below, without requiring any weak continuity assumption. Several special cases are also emphasized. Moreover, a novel definition of Palais–Smale condition, which is more general than the usual one, is presented and a mountain pass theorem is pointed out. As a consequence, multiple critical points theorems are then established. Finally, as an example of applications, an elliptic Dirichlet problem with critical exponent is investigated.