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arXiv · 1812.00951

Surjection and inversion for locally Lipschitz maps between Banach spaces

Olivia Gutú·Jesús A. Jaramillo
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Abstract

We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdifferential, as well as the notion of pseudo-Jacobians in the infinite-dimensional setting, which are the analog of the pseudo-Jacobian matrices defined by Jeyakumar and Luc. Using these notions, we derive our results about existence and uniqueness of solution for nonlinear equations. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context.

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BibTeXRIS

Olivia Gutú, Jesús A. Jaramillo. 2018-12-03. Surjection and inversion for locally Lipschitz maps between Banach spaces. https://doi.org/10.1016/j.jmaa.2019.05.044

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