An oscillation theorem for second order sublinear differential equations

An oscillation criterion is given for the second order sublinear differential equation x + a ( t ) | x | γ sgn ⁡ x = 0 , 0 > γ > 1 x + a(t){\left | x \right |^\gamma }\operatorname {sgn} x = 0,0 > \gamma > 1 , where the coefficient a ( t ) a(t) is not assumed to be nonnegative for all large values of t t . The result extends a condition recently discovered by Butler, Erbe, and Mingarelli for the linear equation.