On strongly monotone flows

• Autorzy: Wolfgang Walter
• Języki publikacji: EN

Abstrakty

EN

M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.

Słowa kluczowe

EN

system of ordinary differential equations; initial value problem; comparison theorem; monotone flow; quasimonotonicity

Kategorie tematyczne

• 34C11: Growth, boundedness
• 34A40: Differential inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 269-274

Daty

wydano

1997

otrzymano

1995-08-21

Twórcy

autor

Wolfgang Walter

• Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Bibliografia

• [1] M. Hirsch, Systems of differential equations that are competitive or cooperative, II: convergence almost everywhere, SIAM J. Math. Anal. 16 (1985), 423-439.
• [2] P. Volkmann, Gewöhnliche Differentialgleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164.
• [3] W. Walter, Gewöhnliche Differentialgleichungen, 5th ed., Springer, 1993.
• [4] T. Ważewski, Systèmes des équations et des inégalités différentielles ordinaires aux deuxièmes membres monotones et leurs applications, Ann. Soc. Polon. Math. 23 (1950), 112-166.