The amplitudes of nonlinear oscillations Original Research Article

Consider the nonlinear, nonautonomous differential equation y″(t)+p(t)f(y(t))=0,t≥t0 where pp is a continuous, positive function and ff is a continuous function such that uf(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.