Given a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a $\sigma$-filtration $\mathcal{F}_*=\{\mathcal{F}_t,t\geq0\}$ on it. The space coincide with the usual conditions. And the random process $B=\{B(t),t\geqslant0\}$ is a one-dimension $\mathcal{F_*}$-Brownian motion. Consider the following one-dimension stochastic differential equation: \begin{equation} \left\{ \begin{aligned} &\mathrm{d}u(t)=\int_{-\infty}^0y(r)u(t+r)\mathrm{d}r\mathrm{d}t+\left(c_3u^3(t)+c_2u^2(t)+c_0\right)\mathrm{d}t\\ &+g(u(t))\mathrm{d}B(t),t\geq0,\\\\ &u(t)=u_0(t),t\leq0. \end{aligned} \right. \end{equation} Here, $u_0(\cdot), y(\cdot)\in L^2\left((-\infty,0],\mathbb{R}\right)$，$g$ satisfies the global Lipschitz condition and linear increasing condition.$c_3<0$ is a constant, $c_2,c_1,c_0$ are random constants.
(1)Give a reasonable definition of the local solution,the maximal local soluton and the global solution as well as their uniqueness to the above eqution.
(2)Give a reasonable condition so that the local solution to the above equation is unique to exist.
(3)Give a reasonable condition so that the global solution to the above eqution is unique to exist.