In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction o...In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction on the entire coefficients associated with Petrenko's deviation of the above equation,we obtain some results and partially address a question posed byⅠ.Laine and C.C.Yang.Furthermore,for the entire solutions f(z)of the difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=F(z),where Aj(z)(j=0,…,n),F(z)are entire functions,we discover a close relationship between the measure of common transcendental directions associated with classical difference operators of f(z)and Petrenko's deviations of the coefficients.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11661043)and the ScienceTechnology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ2200320).
文摘In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction on the entire coefficients associated with Petrenko's deviation of the above equation,we obtain some results and partially address a question posed byⅠ.Laine and C.C.Yang.Furthermore,for the entire solutions f(z)of the difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=F(z),where Aj(z)(j=0,…,n),F(z)are entire functions,we discover a close relationship between the measure of common transcendental directions associated with classical difference operators of f(z)and Petrenko's deviations of the coefficients.
基金Supported by the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)the Hunan Province Science and Technology Project(2012FJ3107)
