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

Došlý, Ondřej; Peña, Simón

J. Inequal. Appl. 2005, No. 5, 535-545 (2005).

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