\L ojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures

摘要

In this paper, we give some {\L}ojasiewicz-type inequalities and a nonsmoothslope inequality on non-compact domains for continuous definable functions inan o-minimal structure. We also give a necessary and sufficicent condition forwhich global error bound exists. Moreover, we point out the relationshipbetween the Palais-Smale condition and this global error bound.