复域差分和差分方程的研究

Study on Complex Differences and Difference Equations

介绍了近十年来复域差分、q-差分、差分方程及q-差分方程的主要研究成果,其中包括亚纯函数对数导数引理的差分模拟;Clunie引理和Mohon'ko引理的差分模拟;慢增长亚纯函数的差分、均差分的零点和不动点的性质;差分多项式的值分布性质;差分Riccati方程与差分Painlevé方程亚纯解的性质;复域q-差分及q-差分方程的解析性质.

The researches on the complex difference, complex q-difference, difference equations and q-difference equations in recent decades are mainly introduced. These results include the difference analogue of the logarithmic derivative; the difference analogue of Clunie lemma; the difference counterpart of Mohon＇ko lemma; the properties on the zeros, fixed-points on complex differences and divided difference of meromorphic functions with small order; the properties on the value distribution of difference polynomials, the properties on the meromorphic solutions of difference Riccati and Painlev6 equations ; the results on q-differences and meromorphic solutions of q-difference e- quations.