On meromorphic solutions of certain type of non-linear differential equations

Abstract

We consider meromorphic solutions of non-linear differential equation of the form f n + Qd(z;f) = p1(z)e 1(z) + p2(z)e 2(z) ; where Qd(z;f) is a differential polynomial in f of degree d ≤ n − 2 with rational functions as its coefficients, p1;p2 are rational functions and 1; 2 are polynomials. More precisely and mainly we have shown the conditions concerning ' = ' 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.