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Asymptotic analysis of positive solutions of a class of third order nonlinear differential equations in the framework of regular variation
Author(s) -
Jaroš Jaroslav,
Takaŝi Kusano,
Tanigawa Tomoyuki
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100296
Subject(s) - sublinear function , mathematics , nonlinear system , variation (astronomy) , asymptotic analysis , class (philosophy) , order (exchange) , mathematical analysis , differential equation , third order , variation of parameters , law , physics , finance , quantum mechanics , artificial intelligence , astrophysics , computer science , political science , economics
This paper is devoted to the asymptotic analysis of the third order sublinear differential equation\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ x^{\prime \prime \prime } + q(t)|x|^{\gamma }\textrm {sgn}\;x = 0, \quad q(t) > 0, \quad 0 < \gamma < 1, \qquad \mathrm{(\textrm {A})} $$ \end{document} in the framework of regular variation. It is shown that in case q ( t ) is nearly regularly varying accurate information can be acquired about the existence of possible positive solutions of (A) and their asymptotic behavior as t → ∞.