Oscillation of delay differential equations

• Autorzy: J. Džurina
• Języki publikacji: EN

Abstrakty

EN

Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument
y'''(t) - q(t)y(τ(t)) = 0
and the oscillation of the second order delay equation of the form
y''(t) + p(t)y(τ(t)) = 0.

Słowa kluczowe

EN

property (B); oscillation

Kategorie tematyczne

• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1997
• Tom: 17
• Numer: 1-2
• Strony: 97-105

Daty

wydano

1997

otrzymano

1998-02-08

Twórcy

autor

J. Džurina

• Department of Mathematical Analysis, Faculty of Sciences,, Safárik University, Jesenná 5, 041 54 Košice, Slovakia

Bibliografia

• [1] J. Chao, On the oscillation of linear differential equations with deviating arguments, Math. in Practice and Theory 1 (1991), 32-40.
• [2] J. Džurina, Asymptotic properties of third order delay differential equations, Czech. Math. J. 45 (1995), 443-448.
• [3] J. Džurina, Asymptotic properties of n-th order differential equations with delayed argument Math. Nachr. 171 (1995), 149-156.
• [4] J. Džurina, Comparison theorems for nonlinear ODE', Math. Slovaca. 42 (1992), 299-315.
• [5] L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation Theory for Functional Differential Equations, Dekker New York 1995.
• [6] L.H. Erbe and B.G. Zhang, Oscillation of first order linear differential equations with deviating arguments, Differential Integral Equations. 1 (1988), 305-314.
• [7] S.R. Grace and B.S. Lalli, Comparison and oscillation theorems for functional differential equations with deviating arguments, Math. Nachr. 144 (1989), 65-79.
• [8] J. Jaros and I.P. Stavroulakis, Oscillation tests for delay equations, Rocky Mountain J. Math., (to appear).
• [9] I.T. Kiguradze, On the oscillation of solutions of the equation $d^mu/dt^m + a(t)|u|^n sign u = 0$, Mat. Sb Russian 65 (1964), 172-187. Russian
• [10] T. Kusano and M. Naito, Comparison theorems for functional differential equations with deviating arguments, J. Math. Soc. Japan. 3 (1981), 509-532.
• [11] T. Kusano, M. Naito and K. Tanaka, Oscillatory and asymptotic behavior of solutions of a class of linear ordinary differential equations, Proc. Roy. Soc. Edinburgh 90 (1981), 25-40.
• [12] M.K. Kwong, Oscillation of first order delay equations, J. Math. Anal. Appl. 156 (1991), 274-286.
• [13] G. Ladas, Sharp conditions for oscillation caused by delay, Applicable Anal. 9 (1979), 93-982
• [14] G. Ladas, V. Lakshmikantham and L.S. Papadakis, Oscillations of Higher-Order Retarded Differential Equations Generated by the Retarded Arguments, Academic Press New York 1972.
• [15] G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker New York 1987.
• [16] W.E. Mahfoud, Comparison theorems for delay differential equations, Pacific J. Math. 83 (1979), 187-197.
• [17] W.E. Mahfoud, Oscillation and asymptotic behavior of solutions of n-th order delay differential equations, J. Diff. Eq. 24 (1977), 75-98.