Recently, C.-C. Yang and L Laine have investigated finite order entire solutions f of non- linear differential-difference equations of the form f^n ＋ L（z, f） -= h, where n ≥ 2 is an integer. In particular, it is k...Recently, C.-C. Yang and L Laine have investigated finite order entire solutions f of non- linear differential-difference equations of the form f^n ＋ L（z, f） -= h, where n ≥ 2 is an integer. In particular, it is known that the equation f（z）^2 ＋ q（z）f（z ＋ 1） = p（z）, where p（z）, q（z） are polynomials, has no transcendental entire solutions of finite order. Assuming that Q（z） is also a polynomial and c E C, equations of the form f（z）^n ＋ q（z）e^Q（Z）f（z ＋ c） = p（z） do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.展开更多
The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum b...The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum between the logarithmic orderρlog(f)and the classical orderρ(f)of a meromorphic function f.展开更多
基金supported by the China Scholarship Council (CSC)supported in part by the Academy of Finland #121281
文摘Recently, C.-C. Yang and L Laine have investigated finite order entire solutions f of non- linear differential-difference equations of the form f^n ＋ L（z, f） -= h, where n ≥ 2 is an integer. In particular, it is known that the equation f（z）^2 ＋ q（z）f（z ＋ 1） = p（z）, where p（z）, q（z） are polynomials, has no transcendental entire solutions of finite order. Assuming that Q（z） is also a polynomial and c E C, equations of the form f（z）^n ＋ q（z）e^Q（Z）f（z ＋ c） = p（z） do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.
基金the support of the China Scholarship Council(Grant No.201806330120)supported by National Natural Science Foundation of China(Grant No.11771090)+1 种基金supported by the National Natural Science Foundation of China(Grants Nos.11971288 and 11771090)Shantou University SRFT(Grant No.NTF18029)。
文摘The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated.Theφ-order is used as a general growth indicator,which covers the growth spectrum between the logarithmic orderρlog(f)and the classical orderρ(f)of a meromorphic function f.
