**V. M. Evtukhov and A. M. Klopot**

##
Asymptotic Behavior of Solutions of Ordinary Differential Equations of n-th
Order with Regularly Varying Nonlinearities

**abstract:**

The conditions of existence and asymptotic for $t\uparrow\omega$ $(\omega\le +\infty$)
representations of one class of monotonic solutions of $n$-th order differential
equations containing in the right-hand side a sum of terms with regularly
varying nonlinearities, are established.

**Mathematics Subject Classification:**
34D05, 34C11, 34C12

**Key words and phrases:** *n*-order differential equation, regularly
varying nonlinearity, monotone solution, existence, asymptotic representation