On the Non-existence of Meromorphic Solutions of Certain Types of Non-linear Differential Equations

In this paper, we study meromorphic solutions of non-linear differential equations of the form f(n) + P-d(f) = p(1)e(alpha 1(z)) + p(2)e(alpha 2(z)), where alpha(1), alpha(2) are polynomials of degree k(>= 1), p(1), p(2) are small meromorphic functions of e(zk), P-d(f) is a differential polynomial in f of degree d with smallmeromorphic functions of f as its coefficients. Some sufficient conditions on the non-existence of meromorphic solutions of such equations are provided. Our results complement some previous results.