Hiroshima Mathematical Journal

Asymptotic analysis of positive solutions of third order nonlinear differential equations

Jaroslav Jaroš, Takaŝi Kusano, and Tomoyuki Tanigawa

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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

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

First available in Project Euclid: 17 March 2014

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Zentralblatt MATH identifier

Primary: 34C11: Growth, boundedness 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]

Third order nonlinear differential equation positive solutions asymptotic behavior regularly varying functions


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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