Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-07-07T11:18:20.888Z Has data issue: false hasContentIssue false

Oscillatory properties of the solutions of linear equations of neutral type

Published online by Cambridge University Press:  17 April 2009

D.D. Bainov
Affiliation:
P.O. Box 45, 1504 Sofia, Bulgaria
A.D. Myshkis
Affiliation:
Plovdiv University, “Paissii Hilendarski”
A.I. Zahariev
Affiliation:
Moscow Institute of Railway Transport Engineers
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper the oscillatory and asymptotic properties of solutions of the equation

are investigated where δ = ±1, τ > 0, σ > 0, the functions r(s) and are non- decreasing and .

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bainov, D.D., Zahariev, A.I. and Myshkis, A.D., ‘Oscillatory properties of the solutions of a class of integro-differential equations of neutral type’, IX Intern. Conf. on Nonlin. Osc 2, pp. 3940 (Naukova Dumka, Kiev, 1984). (in Russian)Google Scholar
[2]Bainov, D.D., Myshkis, A.D. and Zahariev, A.I., ‘Necessary and sufficient conditions for oscillations of the solutions of linear autonomous functional differential equations of neutral type with distributed delay’ (to appear).Google Scholar
[3]Braiton, R., ‘Nonlinear oscillations in a distributed network’, Quart. Appl. Math. 24 (1967), 289301.CrossRefGoogle Scholar
[4]Grammatikopoulos, M.K., Grove, E.A. and Ladas, G., ‘Oscillation and asymptotic behaviour of neutral differential equations with deviating arguments’, Applicable Anal. (to appear).Google Scholar
[5]Grammatikopoulos, M.K., Grove, E.A. and Ladas, G., ‘Oscillations of first order neutral delay differential equations’, J. Math. Anal. Appl. (to appear).Google Scholar
[6]Grammatikopoulos, M.K.Grove, E.A. and Ladas, G., ‘Oscillations and asymptotic behaviour of second order neutral differential equations with deviating arguments’ (to appear).Google Scholar
[7]Hale, J., Theory of functional differential equations (Springer-Verlag, New York, 1977).CrossRefGoogle Scholar
[8]Kolmanovskii, V.B. and Nosov, V.R., Stability and periodic régimes of controllable systems with aftereffect (Moscow, 1981). (in Russian)Google Scholar
[9]Koplatadze, R.G. and Canturia, T.A., ‘On oscillatory and monotonic solutions of first order differential-difference equations with retarded arguments’, Differentsial'nye Uravaneniya 8 (1982), 14631465. (in Russian)Google Scholar
[10]Ladas, G. and Stavroulakis, I.P., ‘On delay differential inequalities of first order’, Funkcial Ekvac. 25 (1982), 105113.Google Scholar
[11]Myshkis, A.D., Linear differential equations with a delaying argument (Moscow, 1972). (in Russian)Google Scholar
[12]Myshkis, A.D., Bainov, D.D. and Zahariev, A.I., ‘Oscillatory and asymptotic properties of a class of operator-differential inequalities’, Proc. Roy. Soc. Edinburgh Sect A 96 (1984), 513.CrossRefGoogle Scholar
[13]Onose, H., ‘Oscillatory properties of the first order differential inequalities with deviating arguments’, Funkcial Ekvac. 26 (1983), 189195.Google Scholar
[14]Zahariev, A.I. and Bainov, D.D., ‘Oscillating properties of the solutions of a class of neutral type functional differential equations’, Bull. Austral. Math. Soc. 22 (1980), 365372.CrossRefGoogle Scholar
[15]Zahariev, A.I. and Bainov, D.D., ‘Oscillating and asymptotic properties of a class of functional differential equations with maxima’, Czechoslovak Math. J. 34 (1984), 247251.Google Scholar