Characterizations of Finite Order Solutions of Circular Type Partial Differential-Difference Equations in \( \mathbb {C}^n \)

This paper employs Nevanlinna value distribution theory in several complex variables to explore the characteristics and form of finite as well as infinite order solutions of Circular-type nonlinear partial differential-difference equations in \(\mathbb {C}^n\) ${\mathbb{C}}^n$ . The results obtained in this paper contribute to the improvement and generalization of some recent results. In addition, illustrative examples are provided to validate the conclusions drawn from the main results. Moreover, we investigate the infinite-order solutions of Circular-type functional equations in \( \mathbb {C}^n \) ${\mathbb{C}}^n$ .