Differential conditions to verify the Jacobian Conjecture
Tom 57 / 1992
Annales Polonici Mathematici 57 (1992), 253-263 DOI: 10.4064/ap-57-3-253-263
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.