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A note on an open problem about the first Painlevé equation
Authors:Hui-zeng Qin  You-min Lu
Institution:(1) Department of Mathematics, Shandong University of Technology, Zibo, 255049, China;(2) Department of Mathematics and Computer Science, Bloomsburg University, Bloomsburg, PA 17821, USA
Abstract:In this note, we apply numerical analysis to the first Painlevé equation, find the conditions for it to have oscillating solutions and therefore solve an open problem posed by Peter A. Clarkson. Supported by the National Natural Science Foundation of China (No.60572073) and School Foundation of Shandong University of Technology (No. 304050).
Keywords:First Painlevé equation  oscillating solutions  numerical method
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