Oscillatory criteria via linearization of half-linear second order delay differential equations

In the paper, we study oscillation of the half-linear second order delay differential equations of the form \[\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.\] We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered e...

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Published inRocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 40; no. 5; pp. 523 - 536
Main Authors Baculíková, Blanka, Džurina, Jozef
Format Journal Article
LanguageEnglish
Published AGH Univeristy of Science and Technology Press 01.01.2020
Subjects
delay
linearization
monotonic properties
oscillation
second order differential equations
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Summary:In the paper, we study oscillation of the half-linear second order delay differential equations of the form \[\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.\] We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.
ISSN:1232-9274
DOI:10.7494/OpMath.2020.40.5.523