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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

${x}^{\text{'}\text{'}}\left(t\right)+a\left(t\right){x}^{\text{'}}\left(t\right)+b\left(t\right)x\left(h\left(t\right)\right)=0$

using a comparison with the integro-differential equation

${y}^{\text{'}}\left(t\right)+{\int }_{{t}_{0}}^{t}{e}^{-{\int }_{s}^{t}a\left(\xi \right)d\xi }b\left(s\right)y\left(h\left(s\right)\right)ds=0·$

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

##### MSC:
 34K05 General theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions of functional-differential equations
##### References:
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