ON MEROMORPHIC SOLUTIONS OF CERTAIN TYPE OF NON-LINEAR DIFFERENTIAL EQUATIONS

We consider meromorphic solutions of non-linear differential equation of the form f(n) + Q(d)(z, f) = p(1)(z)e(alpha 1(z)) + p(2)(z)e(alpha 2(z)), where Q(d)(z, f) is a differential polynomial in f of degree d <= n - 2 with rational functions as its coefficients, p(1), p(2) are rational functions and alpha(1), alpha(2) are polynomials. More precisely and mainly we have shown the conditions concerning alpha(1)'/alpha(2)' that will ensure the existence and forms of the possible meromorphic solutions of the above equation. These results have extended and improved some known results obtained most recently.