ON MEROMORPHIC SOLUTIONS OF FUNCTIONAL-DIFFERENTIAL EQUATIONS

We consider meromorphic solutions of functional-differential equations f((k))(z) = a(f(n) o g) (z) + bf(z) + c, where n, k are two positive integers. Firstly, using an elementary method, we describe the forms of f and g when f is rational and a(not equal 0), b, c are constants. In addition, by employing Nevanlinna theory, we show that g must be linear when f is transcendental and a(not equal 0), b, c are polynomials in C.