UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

doi:10.1016/S0252-9602(14)60018-7

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (2): 444-452.doi: 10.1016/S0252-9602(14)60018-7

• Articles • Previous Articles Next Articles

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

LIU Yong, QI Xiao-Guang

Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China；Department of Physics and Mathematics, Joensuu Campus, University of Eastern Finland, P.O. Box 111, Joensuu FI-80101, Finland； Department of Mathematics, Jinan University, Jinan 250022, China

Received:2012-09-09 Revised:2013-10-16 Online:2014-03-20 Published:2014-03-20
Supported by:
This work was supported by the National Nat-ural Science Foundation of China (10771121, 11301220, 11371225) and the Tianyuan Fund for Mathematics (11226094), the NSF of Shandong Province, China (ZR2012AQ020, ZR2010AM030), the Fund of Doctoral Pro-gram Research of Shaoxing College of Art and Science (20135018), and the Fund of Doctoral Program Research of University of Jinan (XBS1211).

Abstract

CLC Number:

30D35

LIU Yong, QI Xiao-Guang. UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS[J].Acta mathematica scientia,Series B, 2014, 34(2): 444-452.

Trendmd

[1] Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+) and difference equations in the complex plane. Ramanujan J, 2008, 16: 105–129

[2] Chen Z X, Yi H X. On sharing values of meromorphic functions and their differences. Results Math, 2013, 63: 557–565

[3] Goldberg A A, Ostrovskii I V. Distribution of Values of Meromorphic Functions. Mosow: Nauka, 1970

[4] Halburd R G, Korhonen R. Nevanlinna theory for the difference operator. Ann Acad Sci Fenn Math, 2006, 94: 463–478

[5] Halburd R G, Korhonen R. Difference analogue of the lemma on the logarithmic derivative with applications to difference equatons. J Math Anal Appl, 2006, 314: 477–487

[6] Halburd R G, Korhonen R. Finite order solutions and the discrete Painlev´e equations. Proc London Math Soc, 2007, 94: 443–474

[7] Halburd R G, Korhonen R. Meromorphic solutions of difference equations, integrability and the discrete Painlev´e equations. J- Phys A, 2007, 40: 1–38

[8] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964

[9] Heittokangas J, Korhonen R, Laine I, et al. Value sharing results for shift of meromorphic functions, and suffient conditions for periodicity. J Math Anal Appl, 2009, 355: 352–363

[10] Heittokangas J, Korhonen R, Laine I, Rieppo. Uniqueness of meromorphic functions sharing values with their shifts. Complex Var Elliptic Equ, 2011, 56: 81–92

[11] Liu K, Yang L Z. Value distribution of the difference operator. Arch Math, 2009, 92: 270–278

[12] Li J T, Gu Y X. On uniqueness of meromorphic functions and their derivatives. Acta Math Sinica, 2000, 43(1): 87–94

[13] Shibazaki K. Unicity theorem for entire functions of finite order. Japan Men Nat Defense Acad, 1981, 21: 61–71

[14] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Function. Dordrecht: Kluwer, 2003

[15] Yang C C. On two entire functions which together with their first derivative have the same zeros. J Math Anal Appl, 1976, 56(1): 1–6

[16] Yi H X. Uniqueness theorems for meromorphic functions whose N-th derivatives share the same 1-points. Complex variables, 1997, 3(4): 421–436

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Shinji ADACHI, Masataka SHIBATA, Tatsuya WATANABE. A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION [J]. Acta mathematica scientia,Series B, 2018, 38(4): 1121-1142.
[2]	Olivier GUIBÉ, Alip OROPEZA. RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS [J]. Acta mathematica scientia,Series B, 2017, 37(4): 889-910.
[3]	Lingyun GAO. ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS [J]. Acta mathematica scientia,Series B, 2017, 37(1): 187-194.
[4]	Zhendong LUO. A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(2): 385-393.
[5]	Sahbi BOUSSANDEL. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES [J]. Acta mathematica scientia,Series B, 2016, 36(1): 233-243.
[6]	Yang TAN. SEVERAL UNIQUENESS THEOREMS OF ALGEBROID FUNCTIONS ON ANNULI [J]. Acta mathematica scientia,Series B, 2016, 36(1): 295-316.
[7]	Fang LIU. SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS [J]. Acta mathematica scientia,Series B, 2015, 35(2): 477-494.
[8]	LI Xiao-Min, YI Hong-Xun. UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN [J]. Acta mathematica scientia,Series B, 2014, 34(3): 593-609.
[9]	ZHANG Ke-Yu, YI Hong-Xun. THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS [J]. Acta mathematica scientia,Series B, 2014, 34(3): 719-728.
[10]	YE Yu-Lin, DOU Chang-Sheng, JIU Quan-Sen. LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY [J]. Acta mathematica scientia,Series B, 2014, 34(3): 851-871.
[11]	Jacek DZIOK. MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION [J]. Acta mathematica scientia,Series B, 2014, 34(2): 466-472.
[12]	Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH. SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR [J]. Acta mathematica scientia,Series B, 2014, 34(2): 367-379.
[13]	Muhammad ARIF, Janusz SOK′O l, Muhammad AYAZ. SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS [J]. Acta mathematica scientia,Series B, 2014, 34(2): 575-578.
[14]	Helmer A. FRIIS, Steinar EVJE. WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS [J]. Acta mathematica scientia,Series B, 2014, 34(1): 107-124.
[15]	Mirjana STOJANOVIC. REGULARITY OF SOLUTIONS TO NONLINEAR TIME FRACTIONAL DIFFERENTIAL EQUATION [J]. Acta mathematica scientia,Series B, 2013, 33(6): 1721-1735.