Asymptotic behaviors of solutions of second order differential equations (Q1842065)

The paper is concerned with the asymptotic behaviour of solutions of the Emden-Fowler differential equation \(x''(s) + a(s) | x(s) |^{\gamma - 1} x(s) = 0\), \(s > s_ 0 > 0\), where \(a(s)\) is continuous on \([s_ 0, \infty)\) and \(\gamma > 1\) is a constant. Various order estimates for \(x(s)\) for large \(s\) are given for five conditions which \(a(s)\) and \(\gamma\) must satisfy.