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Zbl 1201.34095
Berezansky, Leonid; Dibl{\'\i}k, Josef; Šmarda, Zdeněk
Positive solutions of second-order delay differential equations with a damping term.
(English)
[J] Comput. Math. Appl. 60, No. 5, 1332-1342 (2010). ISSN 0898-1221

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 $$y'(t)+\int_{t_0}^te^{-\int_s^ta(\xi)d\xi}b(s)y(h(s))ds=0.$$ Explicit non-oscillation criteria and comparison type results are derived.
MSC 2000:
*34K05 General theory of functional-differential equations
34K12 Properties of solutions of functional-differential equations

Keywords: second order delay differential equation; positive solution; integro-differential equation

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