I have three equations that are essentially the same equation defined for three time instants. The equations are basically calculating the state of energy of an energy storage facility.
\begin{align} e(t) &= e(0)-d(t)+\eta \cdot c(t);&&t=1\\ e(t) &= e(t-1)-d(t)+\eta\cdot c(t);&&1<t<T\\ e(t) &= 0.5\cdot E;&&t=T \end{align}
$\eta$ and $E$ are parameters; the rest are variables. The equations are defining the value for the same variable $e(t)$. My question is do I include a single variable to define the dual variables for all the equations or I need to define three separate variables with one for each equation. Therefore, if I were to write KKT conditions for the complete formulation, only one or three dual variables will show up.