The amplitudes of nonlinear oscillations (Q2484646)

The authors consider the nonlinear second-order differential equation \[ y''(t)+p(t)f(y(t))=0, ~t\geq t_0, \] where \(p\) is continuous and positive, and \(f\) is continuous with \[ uf(u)>0\text{ for } u\neq 0 \] and \[ \int_0^{\pm\infty}f(u)\,du=\infty. \] They obtain some results about the asymptotic behavior of the amplitudes of all oscillatory solutions of this equation. Combining with other known oscillation results, the authors establish global results for all solutions of the equation.