Meromorphic solutions of three certain types of non-linear difference equations

In this paper, the representations of meromorphic solutions for three types of non-linear difference equations of form f(n)(z) + P-d(z, f) = u(z)e(v(z)), f(n)(z) + P-d(z, f) = p(1)e(lambda z) + p(2)e(-lambda z) and f(n)(z) + P-d(z, f) = p(1)e(alpha 1z) + p(2)e(alpha 2z) are investigated, where n >= 2 is an integer, P-d(z, f) is a difference polynomial in f of degree d <= n - 1 with small coefficients, u(z) is a non-zero polynomial, v(z) is a non-constant polynomial, lambda, p(j), alpha(j) (j = 1, 2) are non-zero constants. Some examples are also presented to show our results are best in certain sense.