Growth results for Painlevé transcendents
Published online by Cambridge University Press: 02 November 2004
Abstract
Painlevé differential equations have been an important topic of research in complex differential equations during the last century, and the last two decades in particular, with many applications not only to pure mathematics but also to physics and engineering. In this paper, we prove that any transcendental solution of the second Painlevé equation $w''\,{=}\,2w^{3}+zw+\alpha$ is of order at least $3/2$, and that any transcendental solution of the fourth Painlevé equation $2ww''\,{=}\,(w')^{2}+3w^{4}+8zw^{3}+4(z^{2}-\alpha )w^{2}+2\beta$ is of order at least $2$.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 3 , November 2004 , pp. 645 - 655
- Copyright
- © 2004 Cambridge Philosophical Society
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