Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x′))′+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x′)]′+[c(t)+μĉ(t)]Φ(x)=0 is conditionally oscillatory, that is, there exists a con...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2011-01, Vol.2011 (2011), p.421-436
Main Authors: Dosly, Ondrej, Fisnarova, Simona
Format: Article
Language:English
Subjects:
Differential equations, Linear
Functional equations
Functions
Perturbation (Mathematics)
Studies
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Summary:We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x′))′+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x′)]′+[c(t)+μĉ(t)]Φ(x)=0 is conditionally oscillatory, that is, there exists a constant γ such that the previous equation is oscillatory if μ-λ>γ and nonoscillatory if μ-λ
ISSN:1085-3375
1687-0409
DOI:10.1155/2011/182827