This article is cited in 3 papers

Precise asymptotic behavior of intermediate solutions of even order nonlinear differential equation in the framework of regular variation

Takaŝi Kusano^a, Jelena Manojlović<sup>b

a</sup> Hiroshima University, Department of Mathematics, Faculty of Science, Higashi-Hiroshima 739-8526, Japan
^b University of Niš, Faculty of Sciences and Mathematics, Department of Mathematics, Višegradska 33, 18000 Niš, Serbia

Abstract: The aim of this paper is to show that if the even-order differential equation of Emden–Fowler type
$$ x^{(2n)}(t)+q(t)|x(t)|^\gamma\operatorname{sgn}x(t)=0,\qquad0<\gamma<1, $$
with regularly varying coefficient $q(t)$ is studied in the framework of regular variation, not only necessary and sufficient conditions for the existence of intermediate regularly varying solutions can be established, but also precise information can be acquired about the asymptotic behavior at infinity of these solutions.

Key words and phrases: even-order differential equation, intermediate solution, regularly varying function, slowly varying function, asymptotic behavior of solutions.

MSC: 34C11, 26A12

Language: English

DOI: 10.17323/1609-4514-2013-13-4-649-666

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