On the meromorphic solutions of a certain type of nonlinear difference-differential equation

Sujoy Majumder; Lata Mahato

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 1, page 73-94
  • ISSN: 0862-7959

Abstract

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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 ) e α 1 ( z ) + p 2 ( z ) e α 2 ( z ) , where P d ( z , f ) is a difference-differential polynomial in f ( z ) of degree d ≤ n - 1 with small functions of f ( z ) as its coefficients, p 1 , p 2 are nonzero rational functions and α 1 , α 2 are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.

How to cite

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Majumder, Sujoy, and Mahato, Lata. "On the meromorphic solutions of a certain type of nonlinear difference-differential equation." Mathematica Bohemica 148.1 (2023): 73-94. <http://eudml.org/doc/299542>.

@article{Majumder2023,
abstract = {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 $d\le n-1$ 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.},
author = {Majumder, Sujoy, Mahato, Lata},
journal = {Mathematica Bohemica},
keywords = {nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory},
language = {eng},
number = {1},
pages = {73-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the meromorphic solutions of a certain type of nonlinear difference-differential equation},
url = {http://eudml.org/doc/299542},
volume = {148},
year = {2023},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 1
SP - 73
EP - 94
AB - 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 $d\le n-1$ 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.
LA - eng
KW - nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory
UR - http://eudml.org/doc/299542
ER -

References

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