Abstract

We consider a continuous function defined on a metric space with values in a Banach space endowed with an order cone. In this setting, we provide an extension of min-max techniques, such as the Mountain pass theorem and Ljusternik-Schnirelman theory, without assuming the order cone to have nonempty interior.

Author information

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

Marco Degiovanni

Dip. di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Dei Musei 41, 25121 Brescia, Italy

m.degiovanni@dmf.unicatt.it

Roberto Lucchetti

Dip. di Matematica, Politecnico di Milano, Via Bonardi 7, 20133 Milano, Italy

rel@komodo.ing.unico.it

Nadezhda Ribarska

Dept. of Mathematics and Informatics, Sofia University, James Bourchier Boul. 5, 1126 Sofia, Bulgaria

ribarska@fmi.uni-sofia.bg

Keywords

  • Vector optimization
  • nonsmooth critical point theory

Mathematics Subject Classification

49J40; 58E05

Suggested citation

M. Degiovanni, R. Lucchetti, N. Ribarska. “Critical Point Theory for Vector Valued Functions.” Journal of Convex Analysis 9 (2002), No. 2, 415–428. https://doi.org/10.68381/jca09024

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press.