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Title:The order of growth of the fourth painleve transcendents
Author(s):Sriponpaew, Boonyong
Director of Research:Hinkkanen, Aimo
Doctoral Committee Member(s):Hinkkanen, Aimo; Loeb, Peter; Nikolaev, Igor; Miles, Joseph B.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):fourth Painlevé equation
order of growth
Abstract:Let w be a transcendental solution of the fourth Painlevé equation w00 = (w0)2 2w + 3 2 w3 + 4zw2 + 2(z2 )w + w : It has a rst integral w02 = w4 + 4zw3 + 4(z2 )w2 2 4wU; where the auxilliary function U satis es U0 = w2 + 2zw: We will consider three speci c cases of limit behaviors of the auxiliary function U outside certain exceptional sets. In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii
Issue Date:2012-05-22
Rights Information:Copyright 2012 Boonyong Sriponpaew
Date Available in IDEALS:2012-05-22
Date Deposited:2012-05

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