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Oscillatory properties of the solutions of impulsive differential equations with a deviating argument and nonconstant coefficients. (English) Zbl 0912.34059

Sufficient conditions are found for the oscillation of all solutions to the impulsive differential equation with a deviating argument \[ x'(t)+p(t)x(t-\tau)=0,\quad t\neq\eta_k, \qquad \Delta x(\tau_k)=b_k x(\tau_k),\quad t=\tau_k, \] where the function \(p\) is not of constant sign.
Reviewer: I.Ginchev (Varna)

MSC:

34K11 Oscillation theory of functional-differential equations
34A37 Ordinary differential equations with impulses
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References:

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[2] I. Györi and G. Ladas, Oscillation theory of delay differential equations with applications , Clarendon Press, Oxford, 1991. · Zbl 0780.34048
[3] G.S. Ladde, V. Lakshmikantham and B.G. Zhang, Oscillation theory of differential equations with deviating arguments , Pure Appl. Math. 110 , Marcel Dekker, New York, 1987. · Zbl 0622.34071
[4] V.N. Shevelo, Oscillations of solutions of differential equations with deviating arguments , Nauk. Dumka, Kiev, 1978 (in Russian). · Zbl 0379.34044
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