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Asymptotic representations of solutions of second-order differential equations

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Abstract

We establish asymptotic representations as t → ω (ω ≤ + ∞) of a class of monotone solutions of the second-order differential equation y″ = f(t, y, y′), where f:[a,ω[× Δ Y0 × Δ Y1 is a continuous function asymptotically close on the considered class of solutions to a function of the form ±p(t)φ 0(y)φ 1(y′) with functions φ 0 and φ 1 regularly varying as y → Y 0 and y′ → Y 1. Here Δ Yi , i ∈ {0, 1}, is a one-sided neighborhood of Y i , and Y i is either zero or ±∞.

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Authors and Affiliations

  1. Odessa National University, Odessa, Ukraine

    V. M. Evtukhov & L. I. Kusik

  2. Odessa National Maritime University, Odessa, Ukraine

    V. M. Evtukhov & L. I. Kusik

Authors
  1. V. M. Evtukhov
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  2. L. I. Kusik
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Original Russian Text © V.M. Evtukhov, L.I. Kusik, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 4, pp. 424–438.

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Evtukhov, V.M., Kusik, L.I. Asymptotic representations of solutions of second-order differential equations. Diff Equat 49, 406–419 (2013). https://doi.org/10.1134/S0012266113040022

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