On meromorphic solution of linear difference-differential equation via partially shared values of meromorphic functions and its growth
Main Article Content
Abstract
In this paper, we investigate shared value problems related to a meromorphic function of hyper order less than one and its linear differencedifferential polynomial. In general, under certain conditions of sharing values of the meromorphic functions and their difference-differential polynomial, a given meromorphic function must satisfy a difference-differential equation. Furthermore, we also study the order of meromorphic solutions of some classes of difference-differential equations.
Article Details
Keywords
Meromorphic function, Nevanlinna theory
References
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[12] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anl. Appl, 355 (2009), 352-363.
[13] N. Li, R. Korhonen and L. Yang, Nevanlinna uniqueness of linear difference polynomials, Rocky Mountain J. Math, 47 (2017), 905-926.
[14] W. Lin, H. Yi, Uniqueness theorems for meromorphic functions, Indian. J. Pure Appl. Math, 35 (2004), 121-132.
[15] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya. J. Math, 161 (2001), 193-206.
[16] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl, 46 (2001), 241-253.
[17] S. Majumder and S. Saha, A Note on the Uniqueness of Certain Types of Differential-Difference Polynomials, Ukr Math J, 73 (2021), 791–810.
[18] X. Qi and L. Yang, Uniqueness of Meromorphic Functions Concerning their Shifts and Derivatives, Comput. Methods. Funct. Theory, 20 (2020), 159-178.
[19] H. X. YI, Uniqueness of meromorphic functions and a question of C.C. Yang, Complex Variables, 14 (1990), 169-176.
[20] X. Zhang, Value sharing of meromorphic functions and some questions of Dyavanal, Front. Math. China, 7 (2012), 161-176.
[21] J. Zhang, L. Z. Yang, Some results related to a conjecture of R. Br¨uck, J. Inequal. Pure Appl. Math, 8 (2007), Article 18.
[2] S. Chen and A. Xu, Uniqueness of Derivatives and Shifts of Meromorphic Functions, Comput. Methods. Funct. Theory, 22 (2022), 197–205.
[3] Y. M. Chiang, S. J. Feng, On the Nevanlinna characteristic f(z + η) and difference equation in the complex plane, Ramanujan. J, 16 (2008), 105-129.
[4] K. S. Charak, R. J. Korhonen, G. Kumar, A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl, 435 (2016), 1241-1248.
[5] R. S. Dyavanal and M. M. Mathai, Uniqueness of DifferenceDifferential Polynomials of Meromorphic Functions, Ukr Math J, 71 (2019), 1032–1042.
[6] G. G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London. Math. Soc, 37(1) (1998), 88-104 .
[7] R. G. Halburd, R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math, 31(2006), 463-478.
[8] R. G. Hulburd, R. J. Korhonen, Difference analogue of the Lemma on the logarithmic derivative with applications to difference equations, J. Math. Anl. Appl, 314 (2006), 477-487.
[9] R. G. Halburd and R. J. Korhonen, Meromorphic solutions of difference equations, integrability and the discrete Painlev’e equations, J. Phys. A: Math. Theor, 40 (2007), R1–R38.
[10] R. Halburd, R. Korhonen, K. Tohge, Holomorphic curves with shiftinvariant hyperplane preimages, Transactions of the American Mathematical Society, 366 (2014), 4267-4298.
[11] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, Uniqueness of meromorphic functions sharing values with their shift, Complex Variables and Elliptic Equations, 56 (2011), 81-92.
[12] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anl. Appl, 355 (2009), 352-363.
[13] N. Li, R. Korhonen and L. Yang, Nevanlinna uniqueness of linear difference polynomials, Rocky Mountain J. Math, 47 (2017), 905-926.
[14] W. Lin, H. Yi, Uniqueness theorems for meromorphic functions, Indian. J. Pure Appl. Math, 35 (2004), 121-132.
[15] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya. J. Math, 161 (2001), 193-206.
[16] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl, 46 (2001), 241-253.
[17] S. Majumder and S. Saha, A Note on the Uniqueness of Certain Types of Differential-Difference Polynomials, Ukr Math J, 73 (2021), 791–810.
[18] X. Qi and L. Yang, Uniqueness of Meromorphic Functions Concerning their Shifts and Derivatives, Comput. Methods. Funct. Theory, 20 (2020), 159-178.
[19] H. X. YI, Uniqueness of meromorphic functions and a question of C.C. Yang, Complex Variables, 14 (1990), 169-176.
[20] X. Zhang, Value sharing of meromorphic functions and some questions of Dyavanal, Front. Math. China, 7 (2012), 161-176.
[21] J. Zhang, L. Z. Yang, Some results related to a conjecture of R. Br¨uck, J. Inequal. Pure Appl. Math, 8 (2007), Article 18.