Moscow Mathematical Journal

Volume 13, Issue 4, October–December 2013 pp. 649–666.

Precise Asymptotic Behavior of Intermediate Solutions of Even Order Nonlinear Differential Equation in the Framework of Regular Variation

Authors: Takaŝi Kusano (1), Jelena Manojlović (2)
Author institution: (1) Professor Emeritus at Hiroshima University, Department of Mathematics, Faculty of Science, Higashi-Hiroshima 739-8526, Japan
(2) University of Niš, Faculty of Science and Mathematics, Department of Mathematics, Višegradska 33, 18000 Niš, Serbia
Summary:

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)|^γ sgn x(t)=0, 0<γ<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 of this equation can be established, but also precise information can be acquired about the asymptotic behavior at infinity of these solutions.

2010 Mathematics Subject Classification. 34C11, 26A12

Keywords: Even-order differential equation, intermediate solution, regularly varying function, slowly varying function, asymptotic behavior of solutions

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