M. A. Belozerova, G. A. Gerzhanovskaya

Asymptotic Representations of Solutions with Slowly Varying Derivatives of Essentially Nonlinear Ordinary Differential Equations of the Second Order

abstract:
Differential equations of the second order with nonlinearities of rather general type that are in some sense near to the power ones are considered. For some class of solutions with derivatives of the first order that are slowly varying functions as the argument tends to the critical point, the conditions of the existence and asymptotic representations are found.

Mathematics Subject Classification: 34C41, 34E10

Key words and phrases: Regular variation, regularly varying function, slowly varying function, nonlinear differential equation, regularly varying solution