Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T06:39:46.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillatory and asymptotic properties of a class of operator-differential inequalities

Published online by Cambridge University Press:  14 November 2011

A. D. Myshkis ,
D. D. Bainov  and
A. I. Zahariev
A. D. Myshkis
Affiliation:
Moscow Institute of Railway Transport Engineers, U.S.S.R.
D. D. Bainov
Affiliation:
University of Plovdiv “Paisii Hilendarski”, Bulgaria
A. I. Zahariev
Affiliation:
University of Plovdiv “Paisii Hilendarski”, Bulgaria
Get access Rights & Permissions [Opens in a new window]

Synopsis

The present paper studies some asymptotic (including oscillatory) properties of the solutions of operator-differential inequalities of the form

where

(the latter symbol denotes the space of locally summable functions).

As an application of the results obtained, theorems are proved for the asymptotic behaviour of the solutions of certain classes of functional-differential and integro-differential neutral-type equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 5 - 13
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Shevelo, V. N.. Oszillyaziya reshenii dijferenziaf nych uravnenii s otkloniayushtimsya argumentom (Kiev: Naukova Dumka, 1978).Google Scholar
2Koplatadze, R. G. and Tshanturiya, T. A.. Ob oscillazionnych svoistvach differenzial’ nych uravnenii s otkonyayushtimsya argumentom (Tbilisi: University of Tbilisi, Institute of Applied Mathematics, 1977).Google Scholar
3Singh, B.. On oscillation and asymptotic non-oscillation of functional retarded equations. Studia Sci. Math. Hungar. 10 1975 (1979), 355–364.Google Scholar
4Grammatikopoulos, M. K., Sficas, J.G. and Staikos, V. A.. Oscillatory properties of strongly superlinear differential equations with deviating arguments. J. Math. Anal. Appl. 67 (1977), 171–197.CrossRefGoogle Scholar
5Kartsatos, A. and Toro, Y.. Oscillation and asymptotic behaviour of forced nonlinear equations. SIAM J. Math. Anal. 10 (1979), 89–95.CrossRefGoogle Scholar
6Lu-San, Chen and Chen-Chin, JehOscillations of n-th order functional differential equations with perturbations. Rend. Istit. Math. Univ. Trieste 11 (1979), 83–90.Google Scholar
7Mahfoud, W. E.. Comparison theorems for delay differential equations. Pacific J. Math. 83 (1979), 187–197.CrossRefGoogle Scholar
8Kitamura, J. and Kusano, T.. Nonlinear oscillations of higher-order functional-differential equations with deviated arguments. J. Math. Anal. Appl. 75 (1980), 135–148.Google Scholar
9Graef, J. R.. Oscillation, nonoscillation and growth of solutions of nonlinear functional differential equations of arbitrary order. Math. Anal. Appi. 60 (1977), 398–409.CrossRefGoogle Scholar
10Marusiak, P.. On oscillation of solutions of differential inequalities with retarded argument. Casopis Pest. Mat. 104 (1979), 281–294.CrossRefGoogle Scholar
11Lu-San, Chen and Chen-Chin, Jeh. On oscillation of solutions of higher-order differential retarded inequalities. Houston J. Math. 5 (1979), 37–14.Google Scholar
12Norkin, S. B.. Oszilazii reshenii differencial'nych uravnenii s otklonyayushtimsya argumentom. In Differential equations with deviating argument, pp. 247–256 (Kiev, 1977).Google Scholar
13Zahariev, 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), 365–372.CrossRefGoogle Scholar
14Kiguradze, I. T.. Nekotorye singulyarnye granichnye zadachi dlya obyknivennych differentialnych uravnenii (Tbilisi: Izd. Tbilisi Univ., 1975).Google Scholar