Mathematica Bohemica, Vol. 143, No. 4, pp. 355-376, 2018
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
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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
