Mathematica Bohemica, first online, pp. 1-26


Entire solutions for systems of Fermat type partial differential equations involving shift and difference operators in $\mathbb C^2$

Goutam HALDAR, Abhijit BANERJE, Ruksana PARVIN

Received July 23, 2025.   Published online March 30, 2026.

Abstract:  We investigate the existence and explicit form of two systems of partial differential equations in $\mathbb{C}^2$: one involving a shift operator and the other a proper difference operator. One of our main results extends a recent finding in the literature, while the other presents a novel contribution. Several illustrative examples are provided to demonstrate the precision and applicability of our results.
Keywords:  entire solution; Fermat-type; differential-difference equation; Nevanlinna theory
Classification MSC:  39A45, 30D35, 32H30, 39A14, 35A20

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Affiliations:   Goutam Haldar (corresponding author), Department of Mathematics, Ghani Khan Choudhury Institute of Engineering and Technology, Narayanpur, Malda, West Bengal 732141, India, e-mail: goutamiit1986@gmail.com; Abhijit Banerje, Ruksana Parvin, Department of Mathematics, University of Kalyani, Kalyani, Nadia-741235, West Bengal, India, e-mail: abanerjee_kal@yahoo.co.in, rukshana7521@gmail.com


 
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