Về hàm phân hình là nghiệm của phương trình vi-sai phân tuyến tính thông qua chung nhau một phần giá trị và độ tăng của nó
Nội dung chính của bài viết
Tóm tắt
Trong bài báo này, chúng tôi nghiên cứu vấn đề chung nhau giá trị của hàm phần hình với siêu bậc bé hơn 1 và đa thức vi-sai phân của nó. Nói một cách tổng thể, dưới những điều kiện về chung nhau một phần giá trị của hàm phân hình và đa thức đạo hàm vi-sai phân, hàm phân hình đã cho phải là nghiệm của phương trình vi-sai phân. Hơn nữa, chúng tôi cũng nghiên cứu độ tăng của nghiệm phân hình của phương trình vi-sai phân.
Chi tiết bài viết
Từ khóa
Hàm phân hình, Lý thuyế Nevanlinna
Tài liệu tham khảo
[1] T. B. Cao and L. Xu, Logarithmic difference lemma in several complex variables and partial difference equations, Annali di Matematica Pura ed Applicata (1923-), 199 (2020), 767–794.
[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.
[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.