The amplitudes of nonlinear oscillations

Consider the nonlinear, nonautonomous differential equationy″(t)+p(t)f(y(t))=0,t≥t0 where p is a continuous, positive function and f is a continuous function such thatuf(u)>0foru≠0, and∫0±∞f(u)du=∞. We obtain some results about the asymptotic behavior of the amplitudes of all oscillatory solutions of this equation. Combining this result with some known oscillation results, we obtain the global results for all solutions of our equation.