@article{7199b2b162ad490c8d528c2541179fff,

title = "Real Solutions of the First Painlev{\'e} Equation with Large Initial Data",

abstract = "We consider three special cases of the initial value problem of the first Painlev{\'e} (PI) equation. Our approach is based on the method of uniform asymptotics introduced by Bassom et al. A rigorous proof of a property of the PI solutions on the negative real axis, recently revealed by Bender and Komijani, is given by approximating the Stokes multipliers. Moreover, we build more precise relation between the large initial data of the PI solutions and their three different types of behavior as the independent variable tends to negative infinity. In addition, some limiting form connection formulas are obtained.",

author = "Long, {W. G.} and Yutian LI and Liu, {S. Y.} and Zhao, {Y. Q.}",

note = "Funding Information: The work of Wen-Gao Long was supported in part by the National Natural Science Foundation of China under Grant Number 11571376 and Guang Dong Natural Science Foundation under Grant Number 2014A030313176. The work of Yu-Tian Li was supported in part by the Hong Kong Research Grants Council [grant numbers 201513 and 12303515] and the HKBU Strategic Development Fund. The work of Sai-Yu Liu was supported in part by the National Natural Science Foundation of China under grant numbers 11326082 and 11401200. The work of Yu-Qiu Zhao was supported in part by the National Natural Science Foundation of China under grant numbers 10871212 and 11571375.",

year = "2017",

month = nov,

doi = "10.1111/sapm.12171",

language = "English",

volume = "139",

pages = "505--532",

journal = "Studies in Applied Mathematics",

issn = "0022-2526",

publisher = "Wiley-Blackwell Publishing Ltd",

number = "4",

}