Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu...In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.展开更多
In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order...In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.展开更多
In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some exam...In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.展开更多
In this paper, we study the growth of solutions of higher order differential equation with meromorphic coefficients, and find some conditions which guarantee that its every nontrivial solution is of infinite order.
In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.
We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ countin...We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.展开更多
We study the argument distribution of infinite order meromorphic functions and obtain distribution theorem which combines the infinite order meromorphic functions with its derived function，
This paper proves the following result:Let f（z） be a meromorphic function in the x-plane with a deficient value,and Δ（θ<sub>k</sub>）(k=1,2,...,q;0（?）θ<sub>1</sub>【θ<sub>2</s...This paper proves the following result:Let f（z） be a meromorphic function in the x-plane with a deficient value,and Δ（θ<sub>k</sub>）(k=1,2,...,q;0（?）θ<sub>1</sub>【θ<sub>2</sub>【...【θ<sub>q</sub>【θ<sub>q+1</sub>=θ<sub>1</sub>+2π) be q rays （1（?）q【∞） starting at the origin,and let n（?）3 be an integer such that for any given positive number ε,0【ε【π/2, （?） where v is a constant independent of ε.If μ【∞,then we have λ（?）π/ω+v, where μ and λ denote the lower order and order of f（z）,respectively,ω=min{θ<sub>k+1</sub>-θ<sub>k</sub>;1（?）k（?）q}, and n（E,f=a） is the number of zeros of f（z）-a in E with multiple zeros being counted with their multiplicities.展开更多
In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain th...In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.展开更多
In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic so...In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.展开更多
In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improv...In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some re...Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.展开更多
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
基金Supported by the NNSFC (10671109)the NSFFC(2008J0190)+1 种基金the Research Fund for Talent Introduction of Ningde Teachers College (2009Y019)the Scitific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
文摘In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.
基金supported by the National Natural Science Foundation of China(10771121,11301220,11371225)the Tianyuan Fund for Mathematics(11226094)+2 种基金the NSF of Shandong Province,China(ZR2012AQ020,ZR2010AM030)the Fund of Doctoral Program Research of Shaoxing College of Art and Science(20135018)the Fund of Doctoral Program Researchof University of Jinan(XBS1211)
文摘In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.
基金The NSF(11201195)of Chinathe NSF(20132BAB201008)of Jiangxi Province
文摘In this paper, we study the growth of solutions of higher order differential equation with meromorphic coefficients, and find some conditions which guarantee that its every nontrivial solution is of infinite order.
基金The NSF(11661044,11201195) of Chinathe NSF(20132BAB201008) of Jiangxi Province
文摘In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.
基金Supported by National Natural Science Foundation of China(Grant Nos.12071047,12171127,11901311)National Key Technologies R&D Program of China(Grant No.2020YFA0713300)。
文摘We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.
文摘We study the argument distribution of infinite order meromorphic functions and obtain distribution theorem which combines the infinite order meromorphic functions with its derived function，
文摘This paper proves the following result:Let f（z） be a meromorphic function in the x-plane with a deficient value,and Δ（θ<sub>k</sub>）(k=1,2,...,q;0（?）θ<sub>1</sub>【θ<sub>2</sub>【...【θ<sub>q</sub>【θ<sub>q+1</sub>=θ<sub>1</sub>+2π) be q rays （1（?）q【∞） starting at the origin,and let n（?）3 be an integer such that for any given positive number ε,0【ε【π/2, （?） where v is a constant independent of ε.If μ【∞,then we have λ（?）π/ω+v, where μ and λ denote the lower order and order of f（z）,respectively,ω=min{θ<sub>k+1</sub>-θ<sub>k</sub>;1（?）k（?）q}, and n（E,f=a） is the number of zeros of f（z）-a in E with multiple zeros being counted with their multiplicities.
基金the National Natural Science Foundation of China(No.10161006)the Natural Science Foundation of Guangdong Province in China(No.04010360)the Brain Pool Program of the Korean Federation of Science and Technology Societies(No.021-1-9)
文摘In this paper, we investigate the growth and fixed points of solutions and their 1st, 2nd derivatives, differential polynomial of second order linear differential equations with meromorphic coefficients, and obtain that the exponents of convergence of these fixed points are all equal to the order of growth.
基金This work is supported by the National Natural Science Foundation of China (No.10161006)the Natural Science Foundation of Jiangxi Province (No.0311043).
文摘In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.
基金This research is supported by the Research Foundation of Doctor Points of China （No. 20060422049） and the National Natural Science Foundation of China （No. 10371065）.
文摘In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.
基金Supported by the National Natural Science Foundation of China (Grant No.10471065)the Natural Science Foundation of Guangdong Province (Grant No.04010474)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.
