Consider the Gelfand triple $V\hookrightarrow H \hookrightarrow V'$ and, for given $T>0$, the Sobolev-Bochner space $$ \mathcal W(0,T) := \{ v \in L^2(0,T;V): \dot v \in L^2(0,T;V')\}. $$
Consider the linear and bounded operator $A\colon V \to V'$, consider $f\in L^2(0,T;V')$, an initial value $\alpha \in H$, and the linear evolution problem:
\begin{align} \dot v(t) + Av(t) &= f(t), \tag{*}\\ v(0) &= \alpha. \end{align}
By means of a Galerkin scheme, one can prove that $(*)$ has a unique solution $v \in \mathcal W(0,T)$, provided $A$ is positive or coercive, i.e. $\langle Au, u\rangle \geq c \|u\|^2$ for all $u\in V$, see, e.g., Ch. 23.9, in the book Nonlinear Functional Analysis, 2A by Zeidler.
Where can I find results on $(*)$ that do not require (strict) positivity of $A$ (but maybe only $\langle Av, v\rangle \geq 0$), trading in the uniqueness of the solutions?