Oscillation theorems for a second order sublinear ordinary differential equation

New oscillation criteria are given for the differential equation \[ u + a ( t ) | u | α sgn ⁡ u = 0 , 0 > α > 1 , u + a(t)|u{|^\alpha }\operatorname {sgn} u = 0,\quad 0 > \alpha > 1, \] where a ( t ) a(t) is allowed to take on negative values for arbitrarily large t t .