Subnormal transcendental meromorphic solutions of delay differential equations

The following two delay differential equations are studied,$\omega {\left(z\right)}^k\sum _{\mu =1}^s{e}_{\mu }\left(z\right)\omega (z+c_{\mu })+a\left(z\right)\frac{{\omega }^{\left(n\right)}\left(z\right)}{\omega \left(z\right)}=R(z,\omega (z\left)\right),$ and$\left(\omega \right(z\left)\omega \right(z+1)-1)\left(\omega \right(z\left)\omega \right(z-1)-1)+a\left(z\right)\frac{{\omega }^{\left(n\right)}\left(z\right)}{\omega \left(z\right)}=R(z,\omega (z\left)\right),$

where $k\ge 0$, $n\ge 1$, $s\ge 1$ are integers, $c_1$, $...$, $c_s$ are nonzero complex numbers, $a\left(z\right)$, $e_1\left(z\right)$, $...$, $e_s\left(z\right)$ are small with respect to ω, $R(z,\omega )$ is rational in ω with small meromorphic coefficients with respect to ω. The necessary conditions for the existence of subnormal transcendental meromorphic solutions of the above two equations are obtained, which extend the previous results from Cao, Chen and Korhonen [2], Halburd and Korhonen [6], Korhonen and Liu [12]. Some examples are given to support these results.