Averaging technique and oscillation criterion for linear and half-linear equations.

Abstract Using a general averaging technique for the generalized adapted Prüfer angle, we prove an oscillation criterion concerning half-linear second order differential equations in the form (∗) t α − 1 r (t) Φ x ′ ′ + t α − 1 − p s (t) Φ (x) = 0 , Φ (x) = | x | p − 1 sgn x , where p > 1 , α ∈ R ∖︀ { p } , and r > 0 , s are continuous functions. We find simple conditions on r , s which imply that Eq. (∗) is oscillatory. The obtained result is new even in the linear case p = 2 for all considered α. [ABSTRACT FROM AUTHOR]