A Linearization Method in Oscillation Theory of Half-linear Second-order Differential Equations
نویسنده
چکیده
Using inequalities for a certain function appearing in the half-linear version of Picone’s identity, we show that oscillatory properties of the half-linear second-order differential equation (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) = |x|p−2x, p > 1, can be investigated via oscillatory properties of a certain associated second-order linear differential equation. This linear equation plays the role of a Sturmian majorant, in a certain sense, if p ≥ 2, and the role of a minorant if p ∈ (1,2].
منابع مشابه
Ondřej Došlý A REMARK ON THE LINEARIZATION TECHNIQUE IN HALF-LINEAR OSCILLATION THEORY∗
We show that oscillatory properties of the half-linear second order differential equation ` r(t)Φ(x′) ́′ + c(t)Φ(x) = 0, Φ(x) = |x|p−2x, p > 1, can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases p ≥ 2 and p ∈ (1, 2]. Our results also improve the oscillation and...
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