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Keywords:
non-oscillation; deviating non-delay equation; singular boundary value problem
non-oscillation; deviating non-delay equation; singular boundary value problem
Summary:
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 $$ u''(x)+\int _0^{\infty }u'(s){\rm d}_sr_1(x,s)+\int _0^{\infty } u(s){\rm d}_sr_0(x,s) = 0. $$
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