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.
Degiovanni, M., Lucchetti, R., Ribarska, N., Critical point theory for vector valued functions, <<JOURNAL OF CONVEX ANALYSIS>>, 2002; (9): 415-428 [https://hdl.handle.net/10807/312913]
Critical point theory for vector valued functions
Degiovanni, Marco
Primo
Conceptualization
;Lucchetti, RobertoSecondo
Conceptualization
;
2002
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.
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