Entire solutions for quadratic trinomial partial differential-difference functional equations in $\mathbb{C}^n$

On solutions of certain compatible systems of quadratic trinomial Partial differential-difference equations

“…, 0)}, a j ∈ C \ {0} for 1 ≤ j ≤ n + 2. For the finite order transcendental entire solutions of the system (7), we obtain the following results.…”

“…. + t jm c jm = 0 and c i is given below in system (7) or (8). We will consider the following systems of quadratic trinomial partial differential-difference equations on several complex variables:…”

“…+ g 2 (y 1 ) are finite order transcendental entire solutions of (7), where g 1 (y 1 ), g 2 (y 1 ) are finite order transcendental entire functions of periods 2s 1 .…”

“…) are finite order transcendental entire solutions of (7), for which condition (A) holds, b 1 = ±a 3 /a 1 and…”

“…A significant number of researchers have demonstrated a keen interest in investigating the Fermat-type equations for entire [8,17,18,21] and meromorphic solutions [20,31] over the past two decades. This has involved the use of a variety of variations of the equation f n (z) + g n (z) = 1, where n ∈ N. Yang and Li [31] were the first to undertake the study of transcendental meromorphic solutions of Fermat-type differential equations on C. Liu [20] was the first who investigated on meromorphic solutions of Fermat-type difference equation as well as differential-difference equations on C. For other leading and recent developments in these directions, we also refer to the reader to [7,22,23,25] and the references therein.…”