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**Oscillation of the solutions to impulsive differential equations and inequalities with a retarded argument.**
*(English)*
Zbl 0922.34059

An impulsive differential equation of first order with a retarded argument is considered.

The main results are devoted to find sufficient conditions to assure that all solutions to the considered equation oscillate. For it, the authors first study the existence of positive (resp. negative) solutions to a couple of related impulsive differential inequalities.

The main results are devoted to find sufficient conditions to assure that all solutions to the considered equation oscillate. For it, the authors first study the existence of positive (resp. negative) solutions to a couple of related impulsive differential inequalities.

Reviewer: Eduardo Liz (Vigo)

### MSC:

34K11 | Oscillation theory of functional-differential equations |

34A37 | Ordinary differential equations with impulses |

### Keywords:

oscillation of the solutions; differential equations with impulses; impulsive differential equations and inequalities
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\textit{D. D. Bainov} et al., Rocky Mt. J. Math. 28, No. 1, 25--40 (1998; Zbl 0922.34059)

### References:

[1] | D.D. Bainov, Yu.I. Domshlak and P.S. Simeonov, Sturmian comparison theory for impulsive differential inequalities and equations , Arch. Math. 67 (1996), 35-49. · Zbl 0856.34033 |

[2] | D.D. Bainov, V. Lakshmikantham and P.S. Simeonov, Theory of impulsive differential equations , World Scientific Publishers, Singapore, 1989. · Zbl 0719.34002 |

[3] | D.D. Bainov and P.S. Simeonov, Systems with impulse effect : Stability, theory and applications , Ellis Horwood Ltd., Chichester, 1989. · Zbl 0683.34032 |

[4] | ——–, Impulsive differential equations : Periodic solutions and applications , Longman, Harlow, 1993. · Zbl 0815.34001 |

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

[6] | I. Györi and G. Ladas, Oscillation theory of delay differential equations with applications , Clarendon Press, Oxford, 1991. · Zbl 0780.34048 |

[7] | G.S. Ladde, V. Lakshmikantham and B.G. Zhang, Oscillation theory of differential equations with deviating arguments , Pure Appl. Math. 110 (1987). · Zbl 0622.34071 |

[8] | 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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