SOME RESULTS ON MEROMORPHIC SOLUTIONS OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS

Abstract

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations fnf (k) + Qd∗ (z, f) = R(z)eα(z) and fnf (k) + Qd(z, f) = p1(z)e α1(z) + p2(z)e2, where Qd∗ (z, f) and Qd(z, f) are differential polynomials in f with small functions as coefficients, of degree d∗ (≤ n − 1) and d (≤ n − 2) respectively, R, p1, p2 are non-vanishing small functions of f , and α, α1, α2 are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.