Finite-Order Solutions of Fermat-Type Partial Differential-Difference Systems in Several Complex Variables
An existence-and-form analysis for pairs of finite-order entire and meromorphic functions of several complex variables that solve certain systems of Fermat-type partial differential-difference equations - equations combining partial derivatives with shifts and difference operators. Students learn to combine Nevanlinna value-distribution theory in several variables with growth-order estimates and difference-operator identities to prove that any finite-order solution pair must take specific exponential forms, refining and generalizing earlier single-equation results to coupled systems.
SOLUTIONS OF SYSTEMS OF CERTAIN FERMAT-TYPE PDDEs RAJU BISWAS AND RAJIB MANDAL Abstract. The
Published in Houston J. Math. 51(1) (2025), 131-162, this paper investigates the existence and explicit forms of pairs of finite-order entire and meromorphic solutions to certain systems of Fermat-ty…