一类差分Painlev$acute{e}$ $I$ 方程的值分布

考虑一类差分Painlev$acute{e}$ $I$方程 $ overline{f}+f+underline{f}=frac{pi_1 z +pi_2}{f}+kappa_1eqno{(*)} $ 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$acute{e}$ $I$方程(*)的有理函数解的存在性及其表示形式, 其中$overline{f}=f(z+1), f=f(z), underline{f}=f(z-1), pi_1 , pi_2 , kappa_1 inmathbb{C}$.

Value distribution of meromorphic solutions of somedifference Painlev$acute{e}$ $I$ equations

The zeros, poles, fixed-points, Borel exceptional value of finite order transcendental meromorphic solutions of difference Painlev$acute{e}$ $I$ equations $$ overline{f}+f+underline{f}=frac{pi_1 z +pi_2}{f}+kappa_1,eqno{(*)} $$ are studied,and the existence,the form of rational solution of the above equation are also considered,where $overline{f}=f(z+1), f=f(z), underline{f}=f(z-1), pi_1 , pi_2 , kappa_1 inmathbb{C}$.