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- Title
ON SOLUTIONS OF CERTAIN COMPATIBLE SYSTEMS OF QUADRATIC TRINOMIAL PARTIAL DIFFERENTIAL-DIFFERENCE EQUATIONS.
- Authors
BISWAS, R.; MANDAL, R.
- Abstract
This paper has involved the use of a variety of variations of the Fermat-type equation fn(z) + gn(z) = 1, where n(≥ 2) ∈ N. Many researchers have demonstrated a keen interest to investigate the Fermat-type equations for entire and meromorphic solutions of several complex variables over the past two decades. Researchers utilize the Nevanlinna theory as the key tool for their investigations. Throughout the paper, we call the pair (f, g) as a finite order entire solution for the Fermat-type compatible system... we consider some earlier systems of certain Fermat-type partial differential-difference equations on C2, especially, those of Xu et al. (Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483(2), 2020) and then construct some systems of certain quadratic trinomial partial differential-difference equations with arbitrary coefficients. Our objective is to investigate the forms of the finite order transcendental entire functions of several complex variables satisfying the systems of certain quadratic trinomial partial differential-difference equations on Cn. These results will extend the further study of this direction.
- Subjects
QUADRATIC equations; PARTIAL differential equations; DIFFERENTIAL-difference equations; QUADRATIC differentials; MEROMORPHIC functions; NEVANLINNA theory
- Publication
Matematychni Studii, 2024, Vol 61, Issue 2, p195
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.61.2.195-213