This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″＋e^-zf′＋Q（z）f=F（z）,whereQ（z）≡h（z）e^cz and c∈R.
In this paper, we deal with the problem of uniqueness of entire or meromorphic functions and obtain some results that are improvements over those of M. Ozawa, H. Ueda, K. Shibazaki and Yi Hongxun. An example shows tha...In this paper, we deal with the problem of uniqueness of entire or meromorphic functions and obtain some results that are improvements over those of M. Ozawa, H. Ueda, K. Shibazaki and Yi Hongxun. An example shows that the results in this paper are sharp.展开更多
In this paper,we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations,and obtain some interesting results.It extends some results concerning complex d...In this paper,we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations,and obtain some interesting results.It extends some results concerning complex differential（difference） equations to the systems of differential-difference equations.展开更多
Let f（z） be an entire function of order λ and of finite lower order μ. If the zeros of f（z） accumulate in the vicinity of a finite number of rays, then （a） λ is finite; （b） for every arbitrary number k<...Let f（z） be an entire function of order λ and of finite lower order μ. If the zeros of f（z） accumulate in the vicinity of a finite number of rays, then （a） λ is finite; （b） for every arbitrary number k<sub>1</sub>】1, there exists k<sub>2</sub>】1 such that T（k<sub>1</sub>r, f）≤k<sub>2</sub>T（r, f） for all r≥r<sub>0</sub>. Applying the above results, we prove that if f（z） is extremal for Yang’s inequality p=g/2, then （c） every deficient value of f（z） is also its asymptotic value; （d） every asymptotic value of f（z） is also its deficient value; （e） λ=μ; （f） ∑a≠∞δ5（a, f）≤1-k（μ）.展开更多
We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Co...We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.展开更多
Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of o...Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.展开更多
In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, ...In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, Hongxun Yi, Meng Chao, C. Y. Fang, M. L. Fang and Junfeng xu.展开更多
基金Tian Yuan Fund for Mathematics (Grant No.10426007)Shanghai Postdoctoral Scientific Program
文摘This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″＋e^-zf′＋Q（z）f=F（z）,whereQ（z）≡h（z）e^cz and c∈R.
基金Supported by the National Natural Science Foundation of China.
文摘In this paper, we deal with the problem of uniqueness of entire or meromorphic functions and obtain some results that are improvements over those of M. Ozawa, H. Ueda, K. Shibazaki and Yi Hongxun. An example shows that the results in this paper are sharp.
文摘In this paper,we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations,and obtain some interesting results.It extends some results concerning complex differential（difference） equations to the systems of differential-difference equations.
文摘Let f（z） be an entire function of order λ and of finite lower order μ. If the zeros of f（z） accumulate in the vicinity of a finite number of rays, then （a） λ is finite; （b） for every arbitrary number k<sub>1</sub>】1, there exists k<sub>2</sub>】1 such that T（k<sub>1</sub>r, f）≤k<sub>2</sub>T（r, f） for all r≥r<sub>0</sub>. Applying the above results, we prove that if f（z） is extremal for Yang’s inequality p=g/2, then （c） every deficient value of f（z） is also its asymptotic value; （d） every asymptotic value of f（z） is also its deficient value; （e） λ=μ; （f） ∑a≠∞δ5（a, f）≤1-k（μ）.
基金supported by the NSFC(12261044)the STP of Education Department of Jiangxi Province of China(GJJ210302)。
文摘We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.
基金supported by the NSF of Shandong Province, China (ZR2010AM030)the NNSF of China (11171013 & 11041005)
文摘Let f be a transcendental meromorphic function and △f（z） = f（z ＋ 1） -- f（z） A number of results are proved concerning the existences of zeros and fixed points of Af（z） and △f（z）/f（z） when f（z） is of order σ（f）=1. Examples show that some of the results are sharp.
文摘In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, Hongxun Yi, Meng Chao, C. Y. Fang, M. L. Fang and Junfeng xu.
