Asymptotic behaviour of solutions of second-order differential equations with rapid varying nonlinearities
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
In the present paper the question of existence and asymptotic, as 𝑡 Ò 𝜔 (𝜔 ¤ 8), behaviour of 𝑃𝜔p𝑌0,𝜆0q-solutions of a binomial non-autonomous 2-nd order differential equation with rapidly varying nonlinearities, as 𝑦 Ñ 𝑌0, where 𝑌0 is equal either to zero or to _8 in case, when 𝜆0 _ 1, is investigated. In this case each of such solutions and its derivative of first order are rapidly varying functions, as 𝑡 Ò 𝜔. There have been obtained new results of necessary and sufficient existence conditions of 𝑃𝜔p𝑌0,1q–solutions of the considered class of essentially nonlinear non autonomous second order ordinary differential equations and asymptotic representations, as 𝑡 Ò 𝜔, of such solutions and their first order derivatives. These results are essentially complement the research, conducted in this direction.
Authors and Affiliations
A. G. Chernikova
Keywords
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