Lithuanian Mathematical Journal

, Volume 53, Issue 1, pp 40–62 | Cite as

Complete asymptotic analysis of positive solutions of odd-order nonlinear differential equation

  • Takaŝi Kusano
  • Jelena V. Manojlović


We study the asymptotic behavior of solutions of the odd-order differential equation of Emden–Fowler type
$$ {x^{{\left( {2n+1} \right)}}}(t)=q(t){{\left| {x(t)} \right|}^{\gamma }}\operatorname{sgn}x(t) $$
in the framework of regular variation under the assumptions that 0 < γ < 1 and q(t) : [a, ∞) → (0, ∞) is regularly varying function. We show that complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity.


odd-order differential equation intermediate solution strongly increasing solution regularly varying function slowly varying function asymptotic behavior of solutions 


34C11 26A12 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Department of Mathematics, Faculty of Science and MathematicsUniversity of NišNišSerbia

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