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

Labovskiy, Sergey; Alves, Manuel

Math. Bohem. 143, No. 4, 355-376 (2018).

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 \[u''(x)+\int_0^{\infty}u'(s)\text{d}_sr_1(x,s)+\int_0^{\infty}u(s)\text{d}_sr_0(x,s)=0.\]

MSC:

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

Keywords:

non-oscillation; deviating non-delay equation; singular boundary value problem

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