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.
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Clarkson, P.A. Painlevé equations-nonlinear special functions. www.uc3m.es/uc3m/dpto/MATEM summerschool/Leganes5.pdf
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Qin, H.Z., Shang, N.N. Asymptotics analysis of a bounded solution to the general third Painlevé equation. MJMS, 18(2): 25–134 (2005)
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Supported by the National Natural Science Foundation of China (No.60572073) and School Foundation of Shandong University of Technology (No. 304050).
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Qin, Hz., Lu, Ym. A note on an open problem about the first Painlevé equation. Acta Math. Appl. Sin. Engl. Ser. 24, 203–210 (2008). https://doi.org/10.1007/s10255-005-5153-4
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DOI: https://doi.org/10.1007/s10255-005-5153-4