## A linearization method in oscillation theory of half-linear second-order differential equations.(English)Zbl 1178.34038

Summary: 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 $(r(t)\Phi(x'))'+c(t)\Phi(x)=0,\quad \Phi(X)=|x|^{p-2}x,\quad p>1,$ 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 $$p\geq 2$$, and the role of a minorant if $$p\in(1,2]$$.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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