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1992 | 57 | 3 | 253-263
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Differential conditions to verify the Jacobian Conjecture

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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.
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,
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