# Institute of Mathematics

## On non-oscillation on semi-axis of solutions of second order deviating differential equations

#### Sergey Labovskiy, Manuel Alves

###### Received March 1, 2017.   First published December 15, 2017.

Abstract:  We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations $u"(x)+\sum_i p_i(x) u'(h_i(x))+\sum_i q_i(x) u(g_i(x)) = 0$ without the delay conditions $h_i(x),g_i(x)\le x$, $i=1,2,\ldots$, and $u"(x)+\int_0^{\infty}u'(s){\rm d}_sr_1(x,s)+\int_0^{\infty} u(s){\rm d}_sr_0(x,s) = 0$.
Keywords:  non-oscillation; deviating non-delay equation; singular boundary value problem
Classification MSC:  34K11, 34K10, 34C10
DOI:  10.21136/MB.2017.0025-17

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Affiliations:   Sergey Labovskiy, Plekhanov Russian University of Economics, Stremyanny laneâ 36, Moscow, 117997, Russia, e-mail: labovski@gmail.com; Manuel Joaquim Alves, Universidade Eduardo Mondlane, Av. Julius Nyerere/Campus 3453, Maputo, Mozambique, e-mail: mjalves.moz@gmail.com

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