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Some comparison criteria in oscillation theory

Part of: Qualitative theory Functional-differential and differential-difference equations

Published online by Cambridge University Press:  09 April 2009

Ch. G. Philos
Ch. G. Philos
Affiliation:
Department of Mathematics University of IoanninaIoannina, Greece
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Abstract

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The purpose of this paper is to establish comparison criteria, by which the oscillatory and asymptotic behavior of linear retarded differential equations of arbitrary order is inherited from the oscillation of an associated second order linear ordinary differential equation. These criteria are new even in the case of ordinary differential equations.

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34K25: Asymptotic theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 2 , April 1984 , pp. 176 - 186
Copyright
Copyright © Australian Mathematical Society 1984

References

Grammatikopoulos, M. K., Sficas, Y. G. and Staikos, V. A. (1979), ‘Oscillatory properties of strongly superlinear differential equations with deviating arguments’, J. Math. Anal. Appl. 67, 171–187.CrossRefGoogle Scholar
Kiguradze, I. T. (1964), ‘On the oscillation of solutions of the equation dm u/dtm + a(t) | u |n sgn u = 0’, (Russian), Mat. Sb. 65, 172–187.Google Scholar
Lovelady, D. L. (1975), ‘An asymptotic analysis of an odd order linear differential equation’, Pacific J. Math. 57, 475–480.CrossRefGoogle Scholar
Lovelady, D. L. (1976), ‘Oscillation and even order linear differential equations’, Rocky Mountain J. Math. 6, 299–304.Google Scholar
Philos, Ch. G. (1981), ‘A new criterion for the oscillatory and asymptotic behavior of delay differential equations’, Bull. Acad. Polon. Sci. Sér. Sci. Mat. 29, 367–370.Google Scholar
Sficas, Y. G. (1973), ‘On oscillation and asymptotic behavior of a certain class of differential equations with retarded argument’, Utilitas Math. 3, 239–249.Google Scholar
Staikos, V. A. and Sficas, Y. G. (1975), ‘Oscillatory and asymptotic characterization of the solutions of differential equations with deviating arguments’, J. London Math. Soc. 10, 39–47.CrossRefGoogle Scholar
Staikos, V. A. (1976), Differential equations with deviating arguments-oscillation theory (unpublished manuscripts).Google Scholar
Swanson, C. A. (1968), Comparison and oscillation theory of linear differential equations (Academic Press, New York, 1968).Google Scholar
Trench, W. F. (1981), ‘An oscillation condition for differential equations of arbitrary order’, Proc. Amer. Math. Soc. 82, 548–552.Google Scholar
Wintner, A. (1951), ‘On the non-existence of conjugate points’, Amer. J. Math. 73, 368–380.CrossRefGoogle Scholar