Geodesic
Some properties of meromorphic solutions of logarithmic order to higher order linear difference equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 15-28.

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This paper is devoted to the study of the growth of solutions of the linear difference equation \begin{gather*} A_n(z)f(z+n)+A_{n-1}(z)f(z+n-1)\\ +\dots+A_1(z)f(z+1)+A_0(z)f(z)=0, \end{gather*} where An(z),…,A0(z) are entire or meromorphic functions of finite logarithmic order. We extend some precedent results due to Liu and Mao, Zheng and Tu, Chen and Shon and others. 
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Benharrat Belaïdi. Some properties of meromorphic solutions of logarithmic order to higher order linear difference equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 15-28. https://geodesic-test.mathdoc.fr/item/BASM_2017_1_a1/

[1] Belaïdi B., “Growth of meromorphic solutions of finite logarithmic order of linear difference equations”, Fasc. Math., 54:5–20 (2015) | Zbl

[2] Cao T. B., Liu K., Wang J., “On the growth of solutions of complex differential equations with entire coefficients of finite logarithmic order”, Math. Reports, 15(65):3 (2013), 249–269 | MR | Zbl

[3] Chen Z. X., Shon K. H., On growth of meromorphic solutions for linear difference equations, Abstr. Appl. Anal., 2013, 2013, 6 pp. | MR

[4] Chern Peter T. Y., “On meromorphic functions with finite logarithmic order”, Trans. Amer. Math. Soc., 358:2 (2006), 473–489 | DOI | MR | Zbl

[5] Chiang Y. M., Feng S. J., “On the Nevanlinna characteristic of $f(z+\eta)$ and difference equations in the complex plane”, Ramanujan J., 16:1 (2008), 105–129 | DOI | MR | Zbl

[6] Gundersen G. G., “Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates”, J. London Math. Soc. (2), 37:1 (1988), 88–104 | DOI | MR | Zbl

[7] Halburd R. G., Korhonen R. J., “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations”, J. Math. Anal. Appl., 314:2 (2006), 477–487 | DOI | MR | Zbl

[8] Halburd R. G., Korhonen R. J., “Nevanlinna theory for the difference operator”, Ann. Acad. Sci. Fenn. Math., 31:2 (2006), 463–478 | MR | Zbl

[9] Hayman W. K., Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964 | MR | Zbl

[10] Heittokangas J., Wen Z. T., “Functions of finite logarithmic order in the unit disc. Part I”, J. Math. Anal. Appl., 415:1 (2014), 435–461 | DOI | MR | Zbl

[11] Heittokangas J., Wen Z. T., “Functions of finite logarithmic order in the unit disc. Part II”, Comput. Methods Funct. Theory, 15:1 (2015), 37–58 | DOI | MR | Zbl

[12] Laine I., Yang C. C., “Clunie theorems for difference and $q$-difference polynomials”, J. Lond. Math. Soc. (2), 76:3 (2007), 556–566 | DOI | MR | Zbl

[13] Liu H., Mao Z., “On the meromorphic solutions of some linear difference equations”, Adv. Difference Equ., 2013 (2013), 133, 12 pp. | DOI | MR

[14] Wen Z. T., “Finite logarithmic order solutions of linear $q$-difference equations”, Bull. Korean Math. Soc., 51:1 (2014), 83–98 | DOI | MR | Zbl

[15] Zheng X. M., Tu J., “Growth of meromorphic solutions of linear difference equations”, J. Math. Anal. Appl., 384:2 (2011), 349–356 | DOI | MR | Zbl

[16] Yang C. C., Yi H. X., Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003 | MR | Zbl