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On the oscillation of differential equations with periodic coefficients. (English) Zbl 0719.34122

The scalar equation \((*)\quad x'(t)+\sum^{m}_{k=1}p_ k(t)x(t-t_ k)=0,\) where \(p_ k\geq 0\) are continuous periodic functions with a common period and \(t_ k\geq 0\) are multiples of this period is examined. A necessary and sufficient condition for the oscillation of all solutions of the equation (*) is established.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[1] L. E. Èl\(^{\prime}\)sgol\(^{\prime}\)ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Academic Press [A Subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Translated from the Russian by John L. Casti; Mathematics in Science and Engineering, Vol. 105.
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[3] G. S. Ladde, V. Lakshmikantham, and B. G. Zhang, Oscillation theory of differential equations with deviating arguments, Monographs and Textbooks in Pure and Applied Mathematics, vol. 110, Marcel Dekker, Inc., New York, 1987. · Zbl 0832.34071
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