Potential and monotone homeomorphisms in Banach spaces

Abstract

Using the Ekeland variational principle and the mountain pass lemma we prove some properties about potential homeomorphisms between a real Banach space and its dual. In particular, we show that a locally monotone homeomorphism is necessarily strictly monotone if it is potential.

Keywords

• browder-minty theorem
• homeomorphisms in banach spaces
• potential operators
• mountain pass lemma
• the ekeland variational principle
• 31c45
• 46t20
• 49j35