Positive solutions of second-order delay differential equations with a damping term

Authors:
Leonid Berezansky;Josef Diblík;Zdenk Šmarda
Affiliations:
Ben-Gurion University of the Negev, Beer-Sheva, Israel;Brno University of Technology, Brno, Czech Republic;Brno University of Technology, Brno, Czech Republic
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 2
Cited 1

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Stability criteria for certain second-order delay differential equations with mixed coefficients

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Abstract

In the paper, 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^te^-^@!^"^s^^^t^a^(^@x^)^d^@xb(s)y(h(s))ds=0. Explicit non-oscillation criteria and comparison type results are derived.