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

Jaroslav Jaroš; Kusano Takaŝi; Jelena Manojlović

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2215-2233
  • ISSN: 2391-5455

Abstract

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Positive solutions of the nonlinear second-order differential equation ( p ( t ) | x ' | α - 1 x ' ) ' + q ( t ) | x | β - 1 x = 0 , α > β > 0 , are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

How to cite

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Jaroslav Jaroš, Kusano Takaŝi, and Jelena Manojlović. "Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation." Open Mathematics 11.12 (2013): 2215-2233. <http://eudml.org/doc/269520>.

@article{JaroslavJaroš2013,
abstract = {Positive solutions of the nonlinear second-order differential equation $(p(t)|x^\{\prime \}|^\{\alpha - 1\} x^\{\prime \})^\{\prime \} + q(t)|x|^\{\beta - 1\} x = 0,\alpha > \beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.},
author = {Jaroslav Jaroš, Kusano Takaŝi, Jelena Manojlović},
journal = {Open Mathematics},
keywords = {Emden-Fowler differential equations; Generalized regularly varying functions; Regularly varying solutions; Slowly varying solutions; Asymptotic behavior of solutions; Positive solutions; generalized regularly varying functions; regularly varying solutions; slowly varying solutions; asymptotic behavior of solutions; positive solutions},
language = {eng},
number = {12},
pages = {2215-2233},
title = {Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation},
url = {http://eudml.org/doc/269520},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Jaroslav Jaroš
AU - Kusano Takaŝi
AU - Jelena Manojlović
TI - Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2215
EP - 2233
AB - Positive solutions of the nonlinear second-order differential equation $(p(t)|x^{\prime }|^{\alpha - 1} x^{\prime })^{\prime } + q(t)|x|^{\beta - 1} x = 0,\alpha > \beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.
LA - eng
KW - Emden-Fowler differential equations; Generalized regularly varying functions; Regularly varying solutions; Slowly varying solutions; Asymptotic behavior of solutions; Positive solutions; generalized regularly varying functions; regularly varying solutions; slowly varying solutions; asymptotic behavior of solutions; positive solutions
UR - http://eudml.org/doc/269520
ER -

References

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