Some Properties of The Solutions of Higher Analogue of The Painlevé Equation
Some Properties of The Solutions of Higher Analogue of The Painlevé Equation
摘要
In this paper, we investigate the value distribution properties for the solution w（z） of higher-order Painlevé equations. We prove that the Nevanlinna＇s second main inequality for w（z） is reduced to an asymptotic equality.
In this paper, we investigate the value distribution properties for the solution w（z） of higher-order Painlevé equations. We prove that the Nevanlinna＇s second main inequality for w（z） is reduced to an asymptotic equality.
基金
Supported by the Mathematical Tianyuan Foundation of China(No.10426007)
the National Natural Science Foundation of China(No.10272017,No.10471028)
参考文献14
-
1Airault, H. Rational solution of Painlev e equation. Studies in Appl. Math., 61:31-53 (1979). 被引量：1
-
2Clunie, J. On integral and meromorphic functions. J.London Math. Soc., 37: (1962). 被引量：1
-
3Gromak, V.I, The first-higher order Painlev e6 equation. Differ. Equations, 35:37-41 (1999). 被引量：1
-
4Gromak, V.I., He, Y. On the solutions of the second Painleve equation of higher order, Proceed. of Math.Inst.of Belarus National Academy of Sci., 4:37-48 (2000). 被引量：1
-
5Hayman, W.K. Meromorphic functions. Clarendon Press, Oxford, 1964. 被引量：1
-
6He, Y. Value distribution of the higher order analogue of the first Painleve equation, Value distribution theory and related topics, edited by G.Barscgian, I.Laine and C.C.Yang, Kluwer Academic Publishers,2004, 209-217. 被引量：1
-
7Laine, I. Nevanlinna theory and complex differential equations. W. de Gruyter, Berlin, 1993. 被引量：1
-
8Li, Y., He, Y. On analytic properties of higher analogue of the second Paiuleve equation.Journal of Mathematical Physics, lss2, 43:1106-1115 (2002). 被引量：1
-
9Mohon'ko, A.Z,Mohon'ko,V.D. Estimates of the nevalinna characteristics of certain classes of meromorphic functions and their applications to differential equations. Sibisk Mat. Zh., 15:1305-1322 (1974) (in Russian). 被引量：1
-
10Painleve, P. Lecons sur la theorie analytique des equations differentielles, Herman, Paris, 1897. 被引量：1
-
1杜海清.(2+1)-维色散长波系统的对称约化与群不变解[J].海南大学学报（自然科学版）,2008,26(3):207-211.
-
2秦惠增,商妮娜.第五类Painlevé方程解的渐近性态分析[J].数学学报（中文版）,2006,49(1):225-230.
-
3邹杰涛,乔节增,侯艳红.第三类Painlevé方程(δ=0或γ=0)解的渐近性态[J].数学的实践与认识,2007,37(7):143-149.
-
4秦惠增,商妮娜.Painlevé方程解的渐近性态的数值分析方法[J].数值计算与计算机应用,2005,26(1):58-64. 被引量：3
-
5商妮娜,秦惠增.非线性常微分方程数值解的渐近表示以及应用[J].山东理工大学学报（自然科学版）,2006,20(1):16-19.
-
6秦惠增,商妮娜.第四类Painlevé方程解的渐近性态分析[J].山东理工大学学报（自然科学版）,2004,18(2):12-15. 被引量：2
-
7李叶舟,袁文俊.第一类Painlevé方程的高阶类似(4_P_1)的解析性质[J].数学物理学报（A辑）,2004,24(6):669-674.
-
8姚若侠,焦小玉,楼森岳.Infinite series symmetry reduction solutions to the modified KdV-Burgers equation[J].Chinese Physics B,2009,18(5):1821-1827. 被引量：3
-
9谷存昌.PⅡ方程的奇异流形方法[J].河南教育学院学报（自然科学版）,2006,15(4):1-2.
-
10李嘉.第四类量子Painlevé方程解的积分表示[J].中国新通信,2014,16(9):63-64.
