Document Type

Pre-Print

Publication Date

10-15-2011

Abstract

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

Document Object Identifier (DOI)

10.1016/j.jmaa.2011.04.092

Publication Information

Journal of Mathematical Analysis and Applications

Included in

Mathematics Commons

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