<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Eugenia N. Petropoulou</style></author><author><style face="normal" font="default" size="100%">Panayiotis D. Siafarikas</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ANALYTIC SOLUTIONS OF THE PAINLEVE EQUATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A25</style></keyword><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">34C11</style></keyword><keyword><style  face="normal" font="default" size="100%">34M55</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2005</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2005</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/9/3/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;For each one of the six well-known Painlev´e equations, it is proved that there exists a unique analytic solution which together with its first two derivatives converge absolutely in a specified region of the complex plane. Moreover, we give a bound of the solution for all six Painlev´e equations and a bound of the first two derivatives of the solution for the last four Painlev´e equations. Finally for all of them we give a region, depending on the initial conditions and the parameters of the equations, in which the solution holds.&lt;/p&gt;
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