Asymptotic behaviour of solutions of nonlinear differential equations (Q810720)

For the nonlinear differential equation \(u^{(n)}=f(t,u),\) where \(f\in C(D,{\mathbb{R}})\), \(D=[T,\infty)\times {\mathbb{R}}\), \(T\geq 1\), \(n\geq 1\), conditions are given for the existence of solutions with the following asymptotic behaviour for \(t\to +\infty:\) \(u(t)=a_ 0t^{n- 1}+...+a_{n-2}t+a_{n-1}+o(1).\)