## 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

### Keywords:

impulsive systems; deviated argument; oscillatory solutions
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### References:

 [1] K. Gopalsamy and B.G. Zhang, On delay differential equations with impulses , J. Math. Anal. Appl. 139 (1989), 110\emdash/122. · Zbl 0687.34065 [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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