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

We show that when n > m, the following delay differential equation f(n)(z) f'(z) + p(z)(f(z + c) - f(z))(m) = r(z)e(q(z)) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of alpha(1), alpha(2) that ensure existence of transcendental meromorphic solutions of the equation f(n)(z) + f(n-2)(z) f'(z) + P-d(z,f) = p(1)(z)e(alpha 1(z)) + p2(z)e(alpha 2(z)()). These results have improved some known theorems obtained most recently by other authors.