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

Labovskiy, Sergey ; Alves, Manuel

Mathematica Bohemica, Tome 143 (2018) no. 4, pp. 355-376

Abstract (VO)

We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \begin {equation*} u''(x)+\sum _i p_i(x) u'(h_i(x))+\sum _i q_i(x) u(g_i(x)) = 0 \end {equation*} without the delay conditions $h_i(x),g_i(x)\le x$, $i=1,2,\ldots $, and $$ u''(x)+\int _0^{\infty }u'(s){\rm d}_sr_1(x,s)+\int _0^{\infty } u(s){\rm d}_sr_0(x,s) = 0. $$

Détail

DOI : 10.21136/MB.2017.0025-17

Classification : 34C10, 34K10, 34K11
Keywords: non-oscillation; deviating non-delay equation; singular boundary value problem

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