复线性微分、差分方程解的振荡性质

In this project, we investigate the oscillation properties of solutions of complex linear differential and difference equations by using the value distribution theory of meromorphic functions. We aim to improve and enrich the theories of complex linear differential and difference equations in the following two aspects:.1) By using the definitions of [p,q]-order、[p,q]-\phi(r) order、proximate order of entire (meromorphic) functions or analytic functions in the unit disc, we investigate the oscillation properties of the solutions of complex linear differential and (q-shift) difference equations, which mainly includes the (regular) growth 、the exponent convergence of zero-sequence and the exponent convergence of fixed-points of the solutions, and the oscillation properties of the differential (difference) polynomials of the solutions..2) We investigate the oscillation properties of the solutions of complex linear differential and difference equations when the coefficients of these equations are analytic functions in an annulus.

本项目主要是利用亚纯函数的值分布理论研究了复线性微分和差分方程解的振荡性质，进一步丰富和完善复线性微分和差分方程理论, 表现在以下2个方面：.1)利用整（亚纯）函数以及单位圆上解析函数的[p,q]级、[p,q]-\phi(r)级、精确级的定义,系统地研究了复线性微分和(q移动)差分方程解的振荡性质，主要包括方程解的(正则)增长性、解的零点、不动点收敛指数以及解的微(差)分多项式的振荡性质。.2)在复线性微分和差分方程系数分别为圆环上的解析函数的情况下，研究了方程解的振荡性质。

本项目主要是利用亚纯函数的值分布理论研究了复线性微分和差分方程解的振荡性质，进一步丰富和完善复线性微分和差分方程理论, 表现在以下2个方面：.1)利用整（亚纯）函数以及单位圆上解析函数的[p,q]级、[p,q]-\phi(r)级、精确级的定义,系统地研究了复线性微分和(q移动)差分方程解的振荡性质,.主要包括方程解的(正则)增长性、解的零点、不动点收敛指数以及解的微(差)分多项式的振荡性质。.2)在复线性微分和差分方程系数分别为圆环上的解析函数的情况下，研究了方程解的振荡性质。