一类差分Painlev\acutee I 方程的值分布

Value distribution of meromorphic solutions \\of somedifference Painlev\acutee I equations

摘要: 考虑一类差分Painlev\acutee I方程 \overlinef+f+\underlinef=\frac\pi_1 z +\pi_2f+\kappa_1\eqno(*) 有限级超越亚纯解的零点、极点、不动点和Borel例外值, 同时也给出了差分Painlev\acutee I方程(*)的有理函数解的存在性及其表示形式, 其中\overlinef=f(z+1), f=f(z), \underlinef=f(z-1), \pi_1 , \pi_2 , \kappa_1 \in\mathbbC.

Abstract: The zeros, poles, fixed-points, Borel exceptional value of finite order transcendental meromorphic solutions of difference Painlev\acutee I equations \overlinef+f+\underlinef=\frac\pi_1 z +\pi_2f+\kappa_1,\eqno(*) are studied,and the existence,the form of rational solution of the above equation are also considered,where \overlinef=f(z+1), f=f(z), \underlinef=f(z-1), \pi_1 , \pi_2 , \kappa_1 \in\mathbbC.