과제정보
This work was financially supported by the National Natural Science Foundation of China (Grant Nos.12171050, 12101068, 12071047).
참고문헌
- S. B. Bank and R. P. Kaufman, On the gamma function and the Nevanlinna characteristic, Analysis 6 (1986), no. 2-3, 115-133. https://doi.org/10.1524/anly.1986.6.23.115
- C. Berenstein, D.-C. Chang, and B. Q. Li, A note on Wronskians and linear dependence of entire functions in Cn, Complex Variables Theory Appl. 24 (1994), no. 1-2, 131-144. https://doi.org/10.1080/17476939408814706
- G. Brosch, Eindeutigkeitssatze fur meromorphe Funktionen, Dissertation, Technical University of Aachen, 1989.
- T. Cao and L. Xu, Logarithmic difference lemma in several complex variables and partial difference equations, Ann. Mat. Pura Appl. (4) 199 (2020), no. 2, 767-794. https://doi.org/10.1007/s10231-019-00899-w
- Z. Chen and Q. Yan, Uniqueness problem of meromorphic functions sharing small functions, Proc. Amer. Math. Soc. 134 (2006), no. 10, 2895-2904. https://doi.org/10.1090/S0002-9939-06-08475-9
- G. G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), no. 2, 299-309. http://projecteuclid.org/euclid.pjm/1102723331 102723331
- W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
- P.-C. Hu and B. Q. Li, Unicity of meromorphic solutions of partial differential equations, J. Math. Sci. (N.Y.) 173 (2011), no. 2, 201-206; translated from Sovrem. Mat. Prilozh. (2010), No. 67, Uravneniya s Chastnymi Proizvodnymi 78-83. https://doi.org/10.1007/s10958-011-0242-9
- P.-C. Hu and B. Q. Li, On meromorphic solutions of nonlinear partial differential equations of first order, J. Math. Anal. Appl. 377 (2011), no. 2, 881-888. https://doi.org/10.1016/j.jmaa.2010.12.004
- P.-C. Hu and B. Q. Li, On meromorphic solutions of linear partial differential equations of second order, J. Math. Anal. Appl. 393 (2012), no. 1, 200-211. https://doi.org/10.1016/j.jmaa.2012.03.012
- P.-C. Hu and B. Q. Li, A note on meromorphic solutions of linear partial differential equations of second order, Complex Anal. Oper. Theory 8 (2014), no. 6, 1173-1182. https://doi.org/10.1007/s11785-013-0314-6
- P.-C. Hu, P. Li, and C.-C. Yang, Unicity of meromorphic mappings, Advances in Complex Analysis and its Applications, 1, Kluwer Academic Publishers, Dordrecht, 2003. https://doi.org/10.1007/978-1-4757-3775-2
- P.-C. Hu and Q.-Y. Wang, On unicity of meromorphic solutions of differential-difference equations, J. Korean Math. Soc. 55 (2018), no. 4, 785-795. https://doi.org/10.4134/JKMS.j170387
- P.-C. Hu and C.-C. Yang, Global solutions of homogeneous linear partial differential equations of the second order, Michigan Math. J. 58 (2009), no. 3, 807-831. https://doi.org/10.1307/mmj/1260475702
- P.-C. Hu and C.-C. Yang, A linear homogeneous partial differential equation with entire solutions represented by Bessel polynomials, J. Math. Anal. Appl. 368 (2010), no. 1, 263-280. https://doi.org/10.1016/j.jmaa.2010.03.048
- R. Korhonen, A difference Picard theorem for meromorphic functions of several variables, Comput. Methods Funct. Theory 12 (2012), no. 1, 343-361. https://doi.org/ 10.1007/BF03321831
- B. Q. Li, Uniqueness of entire functions sharing four small functions, Amer. J. Math. 119 (1997), no. 4, 841-858. https://doi.org/10.1353/ajm.1997.0025
- Y. Li and J. Qiao, The uniqueness of meromorphic functions concerning small functions, Sci. China Ser. A 43 (2000), no. 6, 581-590. https://doi.org/10.1007/BF02908769
- E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung zwei Werte teilen, Results Math. 6 (1983), no. 1, 48-55. https://doi.org/10.1007/BF03323323
- R. Nevanlinna, Einige Eindeutigkeitssatze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), no. 3-4, 367-391. https://doi.org/10.1007/BF02565342
- J. Noguchi and J. Winkelmann, Nevanlinna theory in several complex variables and Diophantine approximation, Grundlehren der mathematischen Wissenschaften, 350, Springer, Tokyo, 2014. https://doi.org/10.1007/978-4-431-54571-2
- M. Ru, Nevanlinna Theory and Its Relation to Diophantine Approximation, World Scientific Publishing Co., Inc., River Edge, NJ, 2001. https://doi.org/10.1142/9789812810519
- S. Shimomura, Entire solutions of a polynomial difference equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 2, 253-266.
- L. Xu and T. Cao, Solutions of complex Fermat-type partial difference and differential-difference equations, Mediterr. J. Math. 15 (2018), no. 6, Paper No. 227, 14 pp. https://doi.org/10.1007/s00009-018-1274-x
- H. Y. Xu and H. Wang, Notes on the existence of entire solutions for several partial differential-difference equations, Bull. Iranian Math. Soc. 47 (2021), no. 5, 1477-1489. https://doi.org/10.1007/s41980-020-00453-y
- K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), no. 2, 225-294. https://doi.org/10.1007/BF02392741
- N. Yanagihara, Meromorphic solutions of some difference equations of higher order, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 21-24. http://projecteuclid.org/euclid.pja/1195516181
- N. Yanagihara, Meromorphic solutions of some difference equations of higher order. II, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 7, 284-286. http://projecteuclid.org/euclid.pja/1195515917
- C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
- Z. Ye, On Nevanlinna's second main theorem in projective space, Invent. Math. 122 (1995), no. 3, 475-507. https://doi.org/10.1007/BF01231453
- Q. D. Zhang, A uniqueness theorem for meromorphic functions with respect to slowly growing functions, Acta Math. Sinica 36 (1993), no. 6, 826-833.
- J. Zheng and R. Korhonen, Studies of differences from the point of view of Nevanlinna theory, Trans. Amer. Math. Soc. 373 (2020), no. 6, 4285-4318. https://doi.org/10.1090/tran/8069