Meromorphic solutions of one certain type of non-linear complex differential equation

In this paper, we are mainly concerned with one certain type of nonlinear complex differential equation f(n)(z) + P-d(z, f) = p(1)e(alpha 1z) + p(2)e(alpha 2z), where p(1), p(2), alpha(1), alpha(2) are non-zero constants and P-d(z, f) is a differential polynomial in f of degree d at most n-1. For this kind of equation, if it admits a meromorphic solution such that N(r, f) = S(r, f), then firstly we give a positive answer to Li's question with a weaker restriction on alpha(1) and alpha(2) than Liu's when alpha(2)/alpha(1) > 0; secondly, we show alpha(1) + alpha(2) = 0 when alpha(2)/alpha(1) < 0.