MEROMORPHIC SOLUTIONS OF SOME NON-LINEAR DIFFERENCE EQUATIONS WITH THREE EXPONENTIAL TERMS

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fn(z) + Pd(z, f) = p1eα1z + p2eα2z + p3eα3z, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, pj (j = 1, 2, 3) are small meromorphic functions of f and αj (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on αj (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.