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We study the global invertibility of non-smooth, locally Lipschitz mapsbetween infinite-dimensional Banach spaces, using a kind of Palais-Smalecondition. To this end, we consider the Chang version of the weightedPalais-Smale condition for locally Lipschitz functionals in terms of the Clarkesubdifferential, as well as the notion of pseudo-Jacobians in theinfinite-dimensional setting, which are the analog of the pseudo-Jacobianmatrices defined by Jeyakumar and Luc. Using these notions, we derive ourresults about existence and uniqueness of solution for nonlinear equations. Inparticular, we give a version of the classical Hadamard integral condition forglobal invertibility in this context.

Surjection and inversion for locally Lipschitz maps between Banach spaces