EXISTENCE OF TRANSCENDENTAL MEROMORPHIC SOLUTIONS ON SOME TYPES OF NONLINEAR DIFFERENTIAL EQUATIONS

We show that when n > m, the following delay differential equation fn(z)f'(z) + p(z)(f(z + c) - f(z))m = r(z)eq(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α1, α2 that ensure existence of transcendental meromorphic solutions of the equation fn(z) + fn-2(z)f'(z) + Pd(z, f) = p1(z)eα1(z) + p2(z)eα2(z). These results have improved some known theorems obtained most recently by other authors.