Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation | Zendy

Takaŝi Kusano | Zendy; Jelena Manojlović | Zendy

Open Access

Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation

Author(s) -

Takaŝi Kusano,

Jelena Manojlović

Publication year - 2012

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2012.1.45

Subject(s) - mathematics , type (biology) , variation (astronomy) , order (exchange) , differential equation , mathematical analysis , differential (mechanical device) , pure mathematics , calculus (dental) , thermodynamics , orthodontics , geology , paleontology , physics , finance , astrophysics , economics , medicine

The asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type x(t) + q(t)|x(t)|sgn x(t) = 0, is studied in the framework of regular variation, under the assumptions that 0 < γ < 1 and q(t) : [a,∞) → (0,∞) is regularly varying function. It is shown that complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity.

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