Abstract
In this paper, we investigate some growth properties of meromorphic solutions of higher-order linear difference equation
where
Acknowledgements
The authors are grateful to the anonymous referee for carefully checking details and also for helpful comments towards the improvement of the paper.
References
[1] B. Belaïdi, Growth and oscillation related to a second order linear differential equation, Math. Commun. 18 (2013), no. 1, 171–184. Search in Google Scholar
[2] B. Belaïdi, Growth of meromorphic solutions of finite logarithmic order of linear difference equations, Fasc. Math. (2015), no. 54, 5–20. 10.1515/fascmath-2015-0001Search in Google Scholar
[3] 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 (2019), no. 4, 1245–1259. Search in Google Scholar
[4]
N. Biswas and S. Tamang,
Growth of solutions to linear differential equations with entire coefficients of
[5] Z.-X. Chen, Growth and zeros of meromorphic solution of some linear difference equations, J. Math. Anal. Appl. 373 (2011), no. 1, 235–241. 10.1016/j.jmaa.2010.06.049Search in Google Scholar
[6] Z.-X. Chen and K. H. Shon, On growth of meromorphic solutions for linear difference equations, Abstr. Appl. Anal. 2013 (2013), Article ID 619296. 10.1155/2013/619296Search in Google Scholar
[7]
Y.-M. Chiang and S.-J. Feng,
On the Nevanlinna characteristic of
[8] Y.-M. Chiang and S.-J. Feng, On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc. 361 (2009), no. 7, 3767–3791. 10.1090/S0002-9947-09-04663-7Search in Google Scholar
[9] I. Chyzhykov, J. Heittokangas and J. Rättyä, Finiteness of ϕ-order of solutions of linear differential equations in the unit disc, J. Anal. Math. 109 (2009), 163–198. 10.1007/s11854-009-0030-3Search in Google Scholar
[10] S. K. Datta and N. Biswas, Growth properties of solutions of complex linear differential-difference equations with coefficients having the same φ-order, Bull. Calcutta Math. Soc. 111 (2019), no. 3, 253–266. Search in Google Scholar
[11] R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477–487. 10.1016/j.jmaa.2005.04.010Search in Google Scholar
[12] W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. Search in Google Scholar
[13] I. Laine and C.-C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556–566. 10.1112/jlms/jdm073Search in Google Scholar
[14] Z. Latreuch and B. Belaïdi, Growth and oscillation of meromorphic solutions of linear difference equations, Mat. Vesnik 66 (2014), no. 2, 213–222. Search in Google Scholar
[15] S. Li and Z.-S. Gao, Finite order meromorphic solutions of linear difference equations, Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 5, 73–76. 10.3792/pjaa.87.73Search in Google Scholar
[16] R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math. 48 (1926), no. 3–4, 367–391. 10.1007/BF02565342Search in Google Scholar
[17] R. Nevanlinna, Analytic Functions, Springer, Berlin, 1970. 10.1007/978-3-642-85590-0Search in Google Scholar
[18]
X. Shen, J. Tu and H. Y. Xu,
Complex oscillation of a second-order linear differential equation with entire coefficients of
[19] X.-M. Zheng and J. Tu, Growth of meromorphic solutions of linear difference equations, J. Math. Anal. Appl. 384 (2011), no. 2, 349–356. 10.1016/j.jmaa.2011.05.069Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston