Oscillatory behavior of the second order noncanonical differential equations

We establish new comparison theorem for deducing oscillation of noncanonical nonlinear differential equation r(t)u′(t)γ′+p(t)uγ(τ(t))=0from that of suitable linear equation y″(t)+p˜(t)u(τ˜(t))=0.Our results are based on Trench's theory of canonical operators and comparison technique.