Vyacheslav M. Evtukhov, Natalia V. Sharay

Asymptotic Behaviour of Solutions of Third-Order Differential Equations with Rapidly Varying Nonlinearities

abstract:
We obtain the existence conditions and asymptotic, as $t\uparrow\omega$ $(\omega\le +\infty)$, representations of one class of solutions of a binomial nonautonomous third-order differential equation with rapidly varying nonlinearity and their derivatives of the first and second order.

Mathematics Subject Classification: 34D05, 34C11

Key words and phrases: Nonlinear third-order differential equation, rapidly changing functions, asymptotic behavior of $P_\omega(Y_0,\lambda_0)$-solutions