## Hiroshima Mathematical Journal

### Asymptotic analysis of positive solutions of third order nonlinear differential equations

#### Abstract

It is shown that an application of the theory of regular variation (in the sense of Karamata) gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third-order nonlinear differential equation $(|x''|^{\alpha-1}x'')' + q(t)|x|^\beta x = 0$, where $\alpha > \beta > 0$ are constants and $q:[a,\infty)\to(0,\infty)$ is a continuous regularly varying function.

#### Article information

Source
Hiroshima Math. J., Volume 44, Number 1 (2014), 1-34.

Dates
First available in Project Euclid: 17 March 2014

https://projecteuclid.org/euclid.hmj/1395061555

Digital Object Identifier
doi:10.32917/hmj/1395061555

Mathematical Reviews number (MathSciNet)
MR3178434

Zentralblatt MATH identifier
1300.34124

#### Citation

Jaroš, Jaroslav; Kusano, Takaŝi; Tanigawa, Tomoyuki. Asymptotic analysis of positive solutions of third order nonlinear differential equations. Hiroshima Math. J. 44 (2014), no. 1, 1--34. doi:10.32917/hmj/1395061555. https://projecteuclid.org/euclid.hmj/1395061555

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