Chang Palais-Smale condition and global inversion

Abstract

Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global diffeomorphism. We also give a version of this fact for a weighted Chang Palais-Smale condition. Finally, we study the relationship of this criterion to some classical global inversion conditions.

10 pages

References in corpus (1)

• On global inverse and implicit functions

Cited by in corpus (2)

• Surjection and inversion for locally Lipschitz maps between Banach spaces
• A Global Diffeomorphism Theorem for Fréchet spaces