Annali di Matematica Pura ed Applicata

, Volume 190, Issue 4, pp 619–644 | Cite as

Asymptotic analysis of Emden-Fowler differential equations in the framework of regular variation

Article

Abstract

Sufficient conditions are established for the existence of slowly varying solution and regularly varying solution of index 1 of the second-order nonlinear differential equation
$$x^{\prime\prime}(t)+q(t)|x(t)|^{\gamma}\,{\rm sgn}\, x(t)=0, \quad \quad (A)$$
where γ is a positive constant different from 1 and q : [a, ∞) → (0, ∞) is a continuous integrable function. We show how an application of the theory of regular variation gives the possibility of determining the precise asymptotic behavior of solutions of both superlinear and sublinear equation (A).

Keywords

Emden-Fowler differential equations Regularly varying solutions Slowly varying solutions Asymptotic behavior of solutions Positive solutions 

Mathematics Subject Classification (2000)

34C11 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of ScienceFukuoka UniversityFukuokaJapan
  2. 2.Faculty of Science and Mathematics, Department of MathematicsUniversity of NišNišSerbia

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