I have the following problem
$$ \max_{[I_i]_{i=0}^{\infty}} \int_{0}^{\infty} \int_{0}^{\eta}\left(A_i(t) h_i(t) - I_i(t)^q \right) di dt $$ subjected to $$ \dot{h}_i(t) = I_i(t) - \delta h_i(t) \hspace{2mm}\forall i \in [0,\eta] $$ where $q >1$ and $\delta \in (0,1)$ and where $A_i >0$ and $\eta >0$.
I'm trying to figure out what are the necessary conditions of this problem, but I don't know the derivation of those conditions.