Olech, C. Global diffeomorphism question and differential equations. (English) Zbl 0754.34049 Qualitative theory of differential equations, 3rd Colloq., Szeged/Hung. 1988, Colloq. Math. Soc. János Bolyai 53, 465-471 (1990). [For the entire collection see Zbl 0695.00015.]It is an old question of the analysis when a continuously differentiable map \(f\) of \(R^ n\) with the assumption \(\text{det} f'(x)\neq0\) \((x\in R^ n)\) is globally one-to-one. The author discusses examples of a relation between this question and ordinary differential equations (e.g. the problem of global asymptotic stability). Reviewer: L.Hatvani (Szeged) Cited in 1 Review MSC: 34D20 Stability of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A60 Ordinary differential inclusions Keywords:Jacobian conjecture; globally one-to-one; global asymptotic stability Citations:Zbl 0695.00015 PDFBibTeX XMLCite \textit{C. Olech}, in: Limiting equations and stability properties for functional differential equations on a fading memory space. . 465--471 (1990; Zbl 0754.34049)