Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least...Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.展开更多
In this paper,we mainly discuss entire solutions of finite order of the following Fermat type differential-difference equation[f(k)(z)]2+[△cf(z)]2=1,and the systems of differential-difference equations of the from ■...In this paper,we mainly discuss entire solutions of finite order of the following Fermat type differential-difference equation[f(k)(z)]2+[△cf(z)]2=1,and the systems of differential-difference equations of the from ■Our results can be proved to be the sufficient and necessary solutions to both equation and systems of equations.展开更多
基金Foundation item： Supported by the NNSF of China（11071083） Supported by the National Natural Science Foundation of Tianyuan Foundation（11126267）
文摘Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.
基金supported by the National Natural Science Foundation of China(11701188)
文摘In this paper,we mainly discuss entire solutions of finite order of the following Fermat type differential-difference equation[f(k)(z)]2+[△cf(z)]2=1,and the systems of differential-difference equations of the from ■Our results can be proved to be the sufficient and necessary solutions to both equation and systems of equations.
