On non-oscillation on semi-axis of solutions of second order deviating differential equations. (English) Zbl 1463.34268

Summary: We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \[u''(x)+\sum_ip_i(x)u'(h_i(x))+\sum_iq_i(x)u(g_i(x))=0\] without the delay conditions \(h_i(x),g_i(x)\leq x\), \(i=1,2,\ldots\), and \[u''(x)+\int_0^{\infty}u'(s)\text{d}_sr_1(x,s)+\int_0^{\infty}u(s)\text{d}_sr_0(x,s)=0.\]


34K11 Oscillation theory of functional-differential equations
34K10 Boundary value problems for functional-differential equations
34K06 Linear functional-differential equations
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