Geodesic
On conditions for the oscillation of solutions to a first-order differential equation with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 72-85

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We establish some new effective conditions for the oscillation of solutions to linear first-order differential equations with aftereffect. We develop a new approach to obtaining oscillation conditions in the form of the upper limit of a function of parameters of an equation. The approach is applied to equations with one and several concentrated delays, and to one with distributed delay. We show the advantages of the new results over known results.
Keywords: functional differential equation, aftereffect, effective tests, several delays, distributed delay, iterative approach.
Mots-clés : oscillation 
@article{IVM_2019_7_a6,
     author = {K. M. Chudinov and V. V. Malygina},
     title = {On conditions for the oscillation of solutions to a first-order differential equation with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--85},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a6/}
}
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K. M. Chudinov; V. V. Malygina. On conditions for the oscillation of solutions to a first-order differential equation with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 72-85. http://geodesic.mathdoc.fr/item/IVM_2019_7_a6/