Oscillation criteria for second order superlinear differential equations

A new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x''(t) + a(t) f(x(t)) = 0, where a(t) is an element of C [t(0), infinity), f(x) is an element of C(R) and xf(x) > 0, f'(x) greater than or equal to 0 for x not equal 0. Furthermore, f(x) also satisfies superlinear condition, which covers the prototype nonlinear function f(x) = \ x \(gamma) sgn x with gamma > 1 known as the Emden-Fowler case. The coefficient a(t) is not assumed to be eventually nonnegative. The oscillation criterion involving integral averages of a(t) give a positive answer to the question given by Wong (Oscillation criterion for second order nonlinear differential equations involving integral averages.