Mathematica Bohemica, Vol. 148, No. 1, pp. 73-94, 2023
On the meromorphic solutions of a certain type of nonlinear difference-differential equation
Sujoy Majumder, Lata Mahato
Received December 6, 2020. Published online March 30, 2022.
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 $d\leq n-1$ 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.
Keywords: nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory
Affiliations: Sujoy Majumder, Department of Mathematics, Raiganj University, Raiganj, West Bengal-733134, India, e-mail: sm05math@gmail.com, Lata Mahato, Department of Mathematics, Mahadevananda Mahavidyalaya, SN Banerjee Rd., Monirampore, Kolkata, West Bengal-700120, India, e-mail: himangshulata@gmail.com