In this paper, we introduce a new modification of the half-linear Prüfer angle. Applying this modification, we investigate the conditional oscillation of the half-linear second order differential equation
where
p>1,
α≠p, and
2ab5159b853cdc3e971afc699" title="Click to view the MathML source">r,s are continuous functions such that
r(t)>0 for large
t. We present conditions on the functions
2ab5159b853cdc3e971afc699" title="Click to view the MathML source">r,s which guarantee that Eq.
(∗) behaves like the Euler type equation
[tα−1Φ(x′)]′+λtα−1−pΦ(x)=0, which is conditionally oscillatory with the oscillation constant
λ0=|p−α|p∕pp.