Asymptotic behaviour of solutions of linear differential equations with delay

• Autorzy: Josef Diblík
• Języki publikacji: EN

Abstrakty

EN

Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.

Słowa kluczowe

EN

linear differential equation with delay; asymptotic behaviour

Kategorie tematyczne

• 34K25: Asymptotic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 2
• Strony: 131-137

Daty

wydano

1993

otrzymano

1992-05-04

poprawiono

1992-10-28

Twórcy

autor

Josef Diblík

• Department of Mathematics, Faculty of Electrical Engineering, Technical University of Brno, Areál Vut Kraví Hora 21 (XV), 602 00 Brno, Czech

Bibliografia

• [1] R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York 1963.
• [2] J. Diblík, On existence and asymptotic behaviour of solutions of singular Cauchy problem for certain system of ordinary differential equations, Fasc. Math. 18 (1988), 51-62.
• [3] J. Hale, Theory of Functional Differential Equations, Springer, New York 1977.
• [4] Ph. Hartman, Ordinary Differential Equations, Wiley, New York 1964.
• [5] V. B. Kolmanovskij and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, 1986.
• [6] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, 1969.
• [7] K. P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138.
• [8] K. P. Rybakowski, A topological principle for retarded functional differential equations of Carathéodory type, ibid. 39 (1981), 131-150.
• [9] T. Ważewski, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279-313.