Olivia Gutú: Chang Palais-Smale condition and global inversion, 293-303

Abstract:

Let $f:X\rightarrow Y$ be a local $C^1$-diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional $x\mapsto \frac{1}{2}\vert f(x)-y\vert^2$ satisfies the Chang Palais-Smale condition for all $y\in Y$, then $f$ is a norm-coercive global $C^1$-diffeomorphism. We also give a version of this fact for a weighted Chang Palais-Smale conditon. Finally, we study the relationship of this criterion to some classical global inversion conditions.

Key Words: global inversion, Palais-Smale condition

2010 Mathematics Subject Classification: Primary 47J07. Secondary 58E05