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May 2006 Asymptotics Analysis of Some Bounded Solution to the General Third Painlevé Equation
Hui-zeng Qin, Ni-na Shang
Missouri J. Math. Sci. 18(2): 125-134 (May 2006). DOI: 10.35834/2006/1802125

Abstract

In this paper, we study the general third Painlevé equation $$y^{\prime \prime }=\frac{y^{\prime 2}}{y}-\frac{y^{\prime }}{x}+\frac{1}{x} (\alpha y^{2}+\beta )+\gamma y^{3}+\frac{\delta }{y}$$ where $\alpha$, $\beta$, $\gamma$, and $\delta$ are real parameters, discuss the boundedness of some solutions when $\gamma <0$ and $\delta >0$, and find an asymptotic representation of a group of oscillating solutions.

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Hui-zeng Qin. Ni-na Shang. "Asymptotics Analysis of Some Bounded Solution to the General Third Painlevé Equation." Missouri J. Math. Sci. 18 (2) 125 - 134, May 2006. https://doi.org/10.35834/2006/1802125

Information

Published: May 2006
First available in Project Euclid: 3 August 2019

zbMATH: 1141.34356
Digital Object Identifier: 10.35834/2006/1802125

Subjects:
Primary: 34L30
Secondary: 34A25 , 34M55

Rights: Copyright © 2006 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.18 • No. 2 • May 2006
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