Geodesic
On the meromorphic solutions of a certain type of nonlinear difference-differential equation
Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 73-94.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation $$ f^{n}(z)+P_{d}(z,f)=p_{1}(z){\rm e}^{\alpha _{1}(z)}+p_{2}(z){\rm e}^{\alpha _{2}(z)}, $$ where $P_d(z,f)$ is a difference-differential polynomial in $f(z)$ of degree $d\leq n-1$ with small functions of $f(z)$ as its coefficients, $p_1$, $p_2$ are nonzero rational functions and $\alpha _1$, $\alpha _2$ are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.
DOI : 10.21136/MB.2022.0186-20
Classification : 30D30, 30D35, 33E30, 34M05
Keywords: nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory 
@article{10_21136_MB_2022_0186_20,
     author = {Majumder, Sujoy and Mahato, Lata},
     title = {On the meromorphic solutions of a certain type of nonlinear difference-differential equation},
     journal = {Mathematica Bohemica},
     pages = {73--94},
     publisher = {mathdoc},
     volume = {148},
     number = {1},
     year = {2023},
     doi = {10.21136/MB.2022.0186-20},
     mrnumber = {4536311},
     zbl = {07655814},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0186-20/}
}
TY  - JOUR
AU  - Majumder, Sujoy
AU  - Mahato, Lata
TI  - On the meromorphic solutions of a certain type of nonlinear difference-differential equation
JO  - Mathematica Bohemica
PY  - 2023
SP  - 73
EP  - 94
VL  - 148
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0186-20/
DO  - 10.21136/MB.2022.0186-20
LA  - en
ID  - 10_21136_MB_2022_0186_20
ER  - 
%0 Journal Article
%A Majumder, Sujoy
%A Mahato, Lata
%T On the meromorphic solutions of a certain type of nonlinear difference-differential equation
%J Mathematica Bohemica
%D 2023
%P 73-94
%V 148
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0186-20/
%R 10.21136/MB.2022.0186-20
%G en
%F 10_21136_MB_2022_0186_20
Majumder, Sujoy; Mahato, Lata. On the meromorphic solutions of a certain type of nonlinear difference-differential equation. Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 73-94. doi : 10.21136/MB.2022.0186-20. http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0186-20/

Cité par Sources :