V. M. Evtukhov and A. M. Klopot

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

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