Differential conditions to verify the Jacobian Conjecture

• Autorzy: Ludwik M. Drużkowski , Halszka K. Tutaj
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

jacobian conditions; global injectivity; global stability

Kategorie tematyczne

• 26B10: Implicit function theorems, Jacobians, transformations with several variables
• 26C10: Polynomials: location of zeros
• 34D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 3
• Strony: 253-263

Daty

wydano

1992

otrzymano

1991-10-30

poprawiono

1992-06-15

Twórcy

autor

Ludwik M. Drużkowski

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

autor

Halszka K. Tutaj

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

Bibliografia

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