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A note on a global invertibility of mappings on Rn
Abstract
We provide sufficient conditions for a mapping ƒ: Rn → Rn to be a global diffeomorphism in case ƒ need not be continuously differentiable. Instead it is assumed to be strictly (Hadamard-like) and Frechet differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.
Mathematics Subject Classication (2010): 57R50, 58E05.
Key words: Global diffeomorphism, local diffeomorphism, inverse function, mountain pass lemma, non-smooth critical point theory.
