ON DELAY-DIFFERENTIAL EQUATIONS WITH SUBNORMAL TRANSCENDENTAL MEROMORPHIC SOLUTIONS

ON DELAY-DIFFERENTIAL EQUATIONS WITH SUBNORMAL TRANSCENDENTAL MEROMORPHIC SOLUTIONS

The necessary conditions on the degree of R(z, ω(z)) for the delay-differential equations $${\omega}(z\,+\,1){\omega}(z\,-\,1)\,+\,a(z){\frac{{\omega}^{(k)}(z)}{{\omega}(z)}}\,=\,R(z,\,{\omega}(z))$$ and $$({\omega}(z\,+\,1)\,+\,{\omega}(z))({\omega}(z\,-\,1)\,+\,{\omega}(z))\,+\,a(z){\frac{{\omega}^{(k)}(z)}{{\omega}(z)}}\,=\,R(z,\,{\omega}(z))$$ to admit a subnormal transcendental meromorphic solution are obtained by using Nevanlinna theory, where k is a positive integer, a(z) is a rational function and R(z, ω) is rational in ω with rational coefficients, which extends and generalizes some previous results. Some examples are given to illustrate these results.