본문 바로가기
KERD
논문KCI 등재

Some results related to complex differential-difference equations of certain types

Kai Liu|Xianjing Dong
대한수학회 (The Korean Mathematical Society)|2014.09|대한수학회보 (Bulletin of the KMS)|제51권 제5호|pp. 1453-1467

0

조회

0

다운로드

3

인용

0

참고문헌

키워드

finite orderdifferential-difference equationsentire solutions
주제분류수학

초록

In this paper, we consider the growth and existence of solutions of differential-difference equations of certain types. We also consider the differential-difference analogues of Br¨uck conjecture and give a short proof on a theorem given by Li, Yang and Yi [18]. Our additional purpose is to explore the similarity or difference on some problems in differential, difference and differential-difference fields.

Abstract

In this paper, we consider the growth and existence of solutions of differential-difference equations of certain types. We also consider the differential-difference analogues of Br¨uck conjecture and give a short proof on a theorem given by Li, Yang and Yi [18]. Our additional purpose is to explore the similarity or difference on some problems in differential, difference and differential-difference fields.

참고문헌 (21)

  1. W. Bergweiler, "Zeros of difference of meromorphic functions", Math. Proc. Cambridge Philos. Soc, 142(1), pp.133~147 (2007)
  2. R. Bellman, "Differential-Difference Equations" (1963), Academic Press
  3. R. Br¨uck, "On entire functions which share one value CM with their first derivative", Results Math, 30(1-2), pp.21~24 (1996)
  4. Z. X. Chen, "Growth and zeros of meromorphic solution of some linear difference equations", J. Math. Anal. Appl, 373(1), pp.235~241 (2011)
  5. Z. X. Chen, "Zeros of entire solutions to complex linear difference equations", Acta Math. Sci. Ser. B Engl. Ed, 32(3), pp.1141~1148 (2012)
  6. Z. X. Chen, "On conjecture of R. Br¨uck concerning the entire function sharing one value CM with its derivative", Taiwanese J. Math, 8(2), pp.235~244 (2004)
  7. Y. M. Chiang, "On the Nevanlinna characteristic of f(z+) and difference equations in the complex plane", Ramanujan J, 16, pp.105~129 (2008)
  8. G. Gundersen, "Entire functions that share one value with one or two of their derivatives", J. Math. Anal. Appl, 223(1), pp.88~95 (1998)
  9. R. G. Halburd, "Difference analogue of the lemma on the logarithmic derivative with applications to difference equations", J. Math. Anal. Appl, 314(2), pp.477~487 (2006)
  10. R. G. Halburd, "Nevanlinna theory for the difference operator", Ann. Acad. Sci. Fenn. Math, 31(2), pp.463~478 (2006)
  11. R. G. Halburd, "Meromorphic solutions of difference equations, integrability and the discrete Painlev´e equations", J. Phys. A, 40(6), pp.1~38 (2007)
  12. W. K. Hayman, "Meromorphic Functions" (1964), Oxford at the Clarendon Press
  13. J. Heittokangas, "Complex difference equations of Malmquist type", Comput. Methods Funct. Theory, 1(1), pp.27~39 (2001)
  14. J. Heittokangas, "Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity", J. Math. Anal. Appl, 355(1), pp.352~363 (2009)
  15. I. Laine, "Nevanlinna Theory and Complex Differential Equations" (1993), Walter de Gruyter
  16. S. Li, "Entire functions sharing one or two finite values CM with their shifts or difference operators", Arch. Math. (Basel), 97(5), pp.475~483 (2011)
  17. B. Q. Li, "On solutions of functional differential equations f′(x) =a(x)f(g(x)) + b(x)f(x) + c(x) in the large", Israel J. Math, 162, pp.335~348 (2007)
  18. X. M. Li, "Entire functions sharing an entire function of smaller order with their shifts", Proc. Japan Acad. Ser. A Math. Sci, 89(2), pp.34~39 (2013)
  19. X. M. Li, "Notes on entire functions sharing an entire function of a smaller order with their difference operators", Arch. Math. (Basel), 99, pp.261~270 (2012)
  20. K. Liu, "Value distribution of the difference operator", Arch. Math. (Basel), 92(3), pp.270~278 (2009)
  21. C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers

관련 논문AI추천

Growth and meromorphic solutions of complex differential and differential-difference equationsPradip Das, Sujoy Majumder대한수학회 · 대한수학회보2025 · 제62권 제6호Growth of solutions of linear differential-difference equations with coefficients having the same logarithmic orderNityagopal Biswas강원경기수학회 · 한국수학논문집2021 · 제29권 제3호A note on meromorphic solutions of complex differential-difference equationsLian-Zhong Yang, Xiao-Guang Qi대한수학회 · 대한수학회보2019 · 제56권 제3호Some results related to differential-difference counterpart of the Br\"{u}ck conjectureBikash Chakraborty, Md. Adud대한수학회 · 대한수학회논문집2024 · 제39권 제1호On solutions to some nonlinear difference and differential equationsPei-Chu Hu, Wei Chen, Yingying Zhang대한수학회 · 대한수학회지2016 · 제53권 제4호On entire solutions of nonlinear difference-differential equationsSheng Li, Songmin Wang대한수학회 · 대한수학회보2013 · 제50권 제5호

이 간행물의 다른 논문 (23건)

Global weak Morrey estimates for some Ultraparabolic operators of Kolmogorov-Fokker-Planck typeMaochun Zhu, Xiaojing Feng, Pengcheng Niupp. 1241-1257Hyperbolicity of chain transitive sets with limit shadowing이승희, Khosro Tajbakhsh, Abbas Fakharipp. 1259-1267Structural stability results for the thermoelasticity of type IIIYan Liupp. 1269-1279On the transcendental entire solutions of a class of differential equationsChungchun Yang, Weiran Lu, Qiuying Lipp. 1281-1289Value distribution of difference operator on meromorphic functionsLian-Zhong Yang, Jie Dingpp. 1291-1297
원문 보기