(untitled) (Analysis in Theory and Applications, 2025)
In this paper, we mainly explore the existence of entire solutions of the quadratic trinomial partial differential-difference equation af^2(z)+2ω f(z)(a_0f(z)+L^k+s_1,2(f(z)))+b(a_0f(z)+L^k+s_1,2(f(z)))^2=e^g(z) by utilizing Nevanlinna’s theory in several complex variables, where g(z) is entire functions in C^n, ω e 0 and a, b, ω ∈ C. Furthermore, we get the exact froms of solutions of the above differential-difference equation when ω = 0. Our results are generalizations of previous results. In addition, some examples are given to illustrate the accuracy of the results.