DOI: https://doi.org/10.11568/kjm.2021.29.3.473

### Growth of solutions of linear differential-difference equations with coefficients having the same logarithmic order

#### Abstract

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

#### Keywords

#### Subject classification

30D35, 34K06, 34K12.#### Sponsor(s)

#### Full Text:

PDF#### References

B. Belaidi, Growth of meromorphic solutions of finite logarithmic order of linear difference equations, Fasc. Math. 54 (2015), 5–20. (Google Scholar)

N. Biswas, S. K. Datta and S. Tamang, On growth properties of transcendental meromorphic solutions of linear differential equations with entire coefficients of higher order, Commun. Korean Math. Soc. 34 (4) (2019), 1245–1259. (Google Scholar)

T.Y. P. Chern, On the maximum modulus and the zeros of an transcendental entire function of finite logarithmic order, Bull. Hong Kong Math. Soc. 2 (1999), 271–278. (Google Scholar)

T.Y. P. Chern, On meromorphic functions with finite logarithmic order, Trans. Am. Math. Soc. 358 (2) (2006), 473–489. (Google Scholar)

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

S. K. Datta and N. Biswas, Growth properties of solutions of complex linear differential-difference equations with coefficients having the same φ-order, Bull. Cal. Math. Soc. 111 (3) (2019), 253– 266. (Google Scholar)

A. Goldberg and I. Ostrovskii, Value Distribution of Meromorphic functions, Translations of Mathematical Monographs, 236. Amer. Math. Soc., Providence, RI, 2008. (Google Scholar)

G. G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1) (1988), 415–429. (Google Scholar)

W. K. Hayman, Meromorphic functions, Clarendon press, Oxford, 1964. (Google Scholar)

I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New York, 1993. (Google Scholar)

I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. 76 (3) (2007), 556–566. (Google Scholar)

H. Liu and Z. Mao, On the meromorphic solutions of some linear difference equations, Adv. Difference Equ. 133 (2013), 1–12. (Google Scholar)

J. Tu and C. F. Yi, On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order, J. Math. Anal. Appl. 340 (1) (2008), 487– 497. (Google Scholar)

J. T. Wen, Finite logarithmic order solutions of linear q-difference equations, Bull. Korean Math. Soc. 51 (1) (2014), 83–98. (Google Scholar)

S. Z. Wu and X. M. Zheng, Growth of meromorphic solutions of complex linear differential-difference equations with coefficients having the same order, Bull. Korean Math. Soc. 34 (6) (2014), 683–695. (Google Scholar)

### Refbacks

- There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr