Growth results for Painlevé transcendents

Aimo Hinkkanen, Ilpo Laine

Research output: Contribution to journalArticlepeer-review

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″ = 2w3 + zw + α is of order at least 3/2, and that any transcendental solution of the fourth Painlevé equation 2ww″ = (w′)2 + 3w4 + 8zw3 + 4(z2 - α)w2 + 2β is of order at least 2.

Original languageEnglish (US)
Pages (from-to)645-655
Number of pages11
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume137
Issue number3
DOIs
StatePublished - Nov 2004

ASJC Scopus subject areas

  • General Mathematics

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