Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In parti...In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe[4]and Bajpai[5].展开更多
This paper investigates the form of complex a lgebraic differential equation with admissible meromorphic solutions and obtains two results which are more precise thatn that of the paper [2].
By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution...By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic func- tions,we investigate the problem of the existence of admissible meromorphic solutions of a type of systems of higher-order algebraic different...Using the Nevanlinna theory of the value distribution of meromorphic func- tions,we investigate the problem of the existence of admissible meromorphic solutions of a type of systems of higher-order algebraic differential equations.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the form of a type of algebraic differential equation with admissible meromorphic solutions and obtain a Malmquist type theorem.
Using the value distribution theory in several complex variables, we extend Malmquist type theorem of algebraic differential equation of Steinmetz to higher-order partial differential equations.
Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic sol...Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.展开更多
We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） ar...We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） are nonzero rational functions, admits a transcendental meromorphic solution f, then Q= C （constant）, the multiplicities of the zeros of R（z） are no greater than 2 and f（z） = √C cos α（z）, where α（z） is a primitive of 1 such that √C cos α（z） is a transcendental meromorphic function. （2） if the differential equation w2 ＋ R（z）（w（k））2 = Q（z）, where k ≥ 2 is an integer and R, Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C （constant）, It（z） ≡ A （constant） and f（z） = √C cos（az ＋ b）, where a2k = A1/A.展开更多
In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）...In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.展开更多
Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of ...Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations.Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.展开更多
Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f,...Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
文摘In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe[4]and Bajpai[5].
文摘This paper investigates the form of complex a lgebraic differential equation with admissible meromorphic solutions and obtains two results which are more precise thatn that of the paper [2].
基金the National Natural Science Foundation of China(10471065)the Natural Science Foundation of Guangdong Province(04010474)
文摘By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.
基金Supported by the National Natural Science Foundation of China (19871050)
文摘Using the Nevanlinna theory of the value distribution of meromorphic func- tions,we investigate the problem of the existence of admissible meromorphic solutions of a type of systems of higher-order algebraic differential equations.
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the form of a type of algebraic differential equation with admissible meromorphic solutions and obtain a Malmquist type theorem.
基金the National Natural Science Foundation of China (10471065)the Natural Science Founda-tion of Guangdong Province (04010474).
文摘Using the value distribution theory in several complex variables, we extend Malmquist type theorem of algebraic differential equation of Steinmetz to higher-order partial differential equations.
基金supported by National Natural Science Foundation of China (Grant No. 10871076)
文摘Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.
基金supported by National Natural Science Foundation of China(Grant Nos.10871011 and 11271179)
文摘We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） are nonzero rational functions, admits a transcendental meromorphic solution f, then Q= C （constant）, the multiplicities of the zeros of R（z） are no greater than 2 and f（z） = √C cos α（z）, where α（z） is a primitive of 1 such that √C cos α（z） is a transcendental meromorphic function. （2） if the differential equation w2 ＋ R（z）（w（k））2 = Q（z）, where k ≥ 2 is an integer and R, Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C （constant）, It（z） ≡ A （constant） and f（z） = √C cos（az ＋ b）, where a2k = A1/A.
文摘In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.
文摘Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations.Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.
文摘Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.
