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Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2#

Xu Hong Yan, Haldar Goutam

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240052

This study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations [formula] and [formula], where L(f) and ˜L(f) are defined in (2.1) and (2.2), respectively, and g(z) is a polynomial in C2. Our results are the extensions of some of the previous results of Liu et al. Also, we exhibit a series of examples to explain that the forms of transcendental entire solutions of finite-order in our results are precise.