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Positive solutions of second-order delay differential equations with a damping term. (English) Zbl 1201.34095

Summary: The existence of positive solutions is studied for the second-order delay differential equation with a damping term

x '' (t)+a(t)x ' (t)+b(t)x(h(t))=0

using a comparison with the integro-differential equation

y ' (t)+ t 0 t e - s t a(ξ)dξ b(s)y(h(s))ds=0·

Explicit non-oscillation criteria and comparison type results are derived.

MSC:
34K05General theory of functional-differential equations
34K12Growth, boundedness, comparison of solutions of functional-differential equations
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