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.
@article{bwmeta1.element.bwnjournal-article-apmv57z3p253bwm,
author = {Ludwik M. Dru\.zkowski and Halszka K. Tutaj},
title = {Differential conditions to verify the Jacobian Conjecture},
journal = {Annales Polonici Mathematici},
volume = {57},
year = {1992},
pages = {253-263},
zbl = {0778.34038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p253bwm}
}
Ludwik M. Drużkowski; Halszka K. Tutaj. Differential conditions to verify the Jacobian Conjecture. Annales Polonici Mathematici, Tome 57 (1992) pp. 253-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p253bwm/
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