R. P. Agarwal, R. Grace

On the Oscillation of Certain Second Order Differential Equations

Some new criteria for the oscillation of all solutions of second order equations of the form $$ \l(a(t)|y'(t)|^{\sigma-1}y'(t)\r)'+q(t)|y(t)|^\sigma~\sgn y(t)=0, \quad \sigma>1, $$ are established. The obtained results extend, unify and corollate many of the known oscillation criteria for second order equations.