Application on Surjection and Inversion for Locally Lipschitz Maps between closer Banach Spaces

An application on the work of O. Gutú, J.A. Jaramil lo [39] for the validity of the study of the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional closer Banach spaces, using the tool of Palais-Smale condition. So we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdifferential, the method of pseudo- Jacobians in the infinitedimensional closer setting, which are the analog of the pseudo-Jacobian matrices defined by Jeyakumar and Luc. Standing on all these, we show the existence and uniqueness of solution for certain nonlinear equations defined by locally Lipschitz mappings. We also show a global surjection theorem for locally Lipschitz maps in terms of pseudo-Jacobians.