Geodesic
On some properties of ultrametric meromorphic solutions of difference equations of Malmquist type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 24-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathbb{K}$ be a complete ultrametric algebraically closed field of characteristic zero and let $\mathcal{M}(\mathbb{K})$ be the field of meromorphic functions in all $\mathbb{K}$. In this paper, using the ultrametric Nevanlinna theory, we investigate the growth of transcendental meromorphic solutions of some ultrametric difference equations. These difference equations arise from the analogue study of the differential equation of Malmquist type. We also give some characterizations of the order of growth for transcendental meromorphic solutions of such equations.
Keywords: Nevanlinna theory, ultrametric meromorphic solution, difference equations, order of growth. 
@article{IVM_2022_8_a1,
     author = {Salih Bouternikh and Tahar Zerzaihi},
     title = {On some properties of ultrametric meromorphic solutions of difference equations of {Malmquist} type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {24--33},
     publisher = {mathdoc},
     number = {8},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_8_a1/}
}
TY  - JOUR
AU  - Salih Bouternikh
AU  - Tahar Zerzaihi
TI  - On some properties of ultrametric meromorphic solutions of difference equations of Malmquist type
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 24
EP  - 33
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_8_a1/
LA  - ru
ID  - IVM_2022_8_a1
ER  - 
%0 Journal Article
%A Salih Bouternikh
%A Tahar Zerzaihi
%T On some properties of ultrametric meromorphic solutions of difference equations of Malmquist type
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 24-33
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2022_8_a1/
%G ru
%F IVM_2022_8_a1
Salih Bouternikh; Tahar Zerzaihi. On some properties of ultrametric meromorphic solutions of difference equations of Malmquist type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 24-33. http://geodesic.mathdoc.fr/item/IVM_2022_8_a1/

[1] Li P., Yang C. C., “Meromorphic solutions of functional equations with nonconstant coefficients”, Proc. Japan Acad. Ser. A, 82:2-10 (2007), 183–186 | MR

[2] Bourourou S., Boutabaa A., Zerzaihi T., “On the growth of solutions of difference equations in ultrametric fields”, Indag. Math. (N.S.), 27:1 (2016), 112–123 | DOI | MR | Zbl

[3] Boutabaa A., “Theorie de Nevanlinna $p$-adique ($p$-adic Nevanlinna theory)”, Manuscripta Math., 67:3 (1990), 251–269 | DOI | MR | Zbl

[4] Boutabaa A., “Applications de la théorie de Nevanlinna $p$-adique”, Collect. Math., 42:1 (1991), 75–93 | MR | Zbl

[5] Boutabaa A., Escassut A., “Applications of the $p$-adic Nevanlinna theory to functional equations”, Ann. Inst. Fourier, 50:3 (2000), 751–766 | DOI | MR | Zbl

[6] Escassut A., Boussaf K., Boutabaa A., “Order, type and cotype of growth for $p$-adic entire functions, $p$-Adic Numbers Ultrametric”, Anal. Appl., 8:4 (2016), 280–297 | MR | Zbl

[7] Hu P.C., Yang C. C., Meromorphic functions over non-Archimedean fields, Springer Science, 2000 | MR

[8] Khoai H. H., “On $p$-adic meromorphic functions”, Duke Math. J., 50:3 (1983), 695–711 | DOI | MR | Zbl

[9] Ru M., “A note on $p$-adic Nevanlinna theory”, Proc. Am. Math. Soc., 129:5 (2001), 1263–1269 | MR | Zbl

[10] Ablowitz M. J., Halburd R., Herbst B., “On the extension of the Painlevé property to difference equations”, Nonlin., 13:3 (2000), 889–905 | DOI | MR | Zbl

[11] Heittokangas J., Korhonen R., Laine I., Rieppo J., Tohge K., “Complex difference equations of Malmquist type”, Comput. Methods Funct. Theory, 1:1 (2001), 27–39 | DOI | MR | Zbl

[12] Katok S., $p$-adic Analysis Compared with Real, Amer. Math. Soc., 2007 | MR | Zbl

[13] Zerzaihi T., Kecies M., Michael K., “Hensel codes of square roots of $p$-adic numbers”, Appl. Anal. Discrete Math., 4:1 (2010), 32–44 | DOI | MR | Zbl

[14] Robert A., A course in $p$-adic analysis, Springer Science, N. Y., 2013 | MR

[15] Mokhon'ko A.Z., “On the Nevanlinna characteristics of some meromorphic functions”, Theory of Functions, Functional Anal. and Their Appl., Kharkiv, 14 (1971), 83–87 | Zbl