In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equationsf(z)n+ P_(n-1)(f) = 0,where n ≥ 2 and P_(n-1)(f) is a difference polynomial of degree at most n- 1 in f with small functions as coefficients. Moreover, we give two examples to show that one conjecture proposed by Yang and Laine [2] does not hold in general if the hyper-order of f(z) is no less than 1.
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