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

Leonid Berezansky; Josef Diblík; Zdeněk Šmarda

doi:10.1016/j.camwa.2010.06.014

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

Leonid Berezansky, Josef Diblík, Zdeněk Šmarda

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t) + a(t)ẋ(t) + b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t) + ∫_t0^t e ^{-∫ts a(ξ)dξ} b(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived.

Original language	English
Pages (from-to)	1332-1342
Number of pages	11
Journal	Computers and Mathematics with Applications
Volume	60
Issue number	5
DOIs	https://doi.org/10.1016/j.camwa.2010.06.014
State	Published - 1 Jan 2010

Keywords

Integro-differential equation
Positive solution
Second order delay differential equation

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2010.06.014

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title = "Positive solutions of second-order delay differential equations with a damping term",

abstract = "In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t) + a(t)ẋ(t) + b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t) + ∫t0t e -∫ts a(ξ)dξ b(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived.",

keywords = "Integro-differential equation, Positive solution, Second order delay differential equation",

author = "Leonid Berezansky and Josef Dibl{\'i}k and Zden{\v e}k {\v S}marda",

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T1 - Positive solutions of second-order delay differential equations with a damping term

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Šmarda, Zdeněk

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t) + a(t)ẋ(t) + b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t) + ∫t0t e -∫ts a(ξ)dξ b(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived.

AB - In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t) + a(t)ẋ(t) + b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t) + ∫t0t e -∫ts a(ξ)dξ b(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived.

KW - Integro-differential equation

KW - Positive solution

KW - Second order delay differential equation

UR - http://www.scopus.com/inward/record.url?scp=78049262422&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2010.06.014

DO - 10.1016/j.camwa.2010.06.014

M3 - Article

AN - SCOPUS:78049262422

SN - 0898-1221

VL - 60

SP - 1332

EP - 1342

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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