For $i=1,\ldots, n$, let $c_i:\mathbb R\to [0,1]$ be continuous, $a_i, b_i>0$ and $\mu_i \ge 0$. Consider the following Volterra equation:
$$f(t)=\sum_{i=1}^n c_i(t)\left[\mu_i + \int_{-\infty}^t a_ie^{-b_i(t-s)}f(s) ds\right],\quad \forall t\in\mathbb R.$$
Does this equation admits a unique solution (even under reasonably stronger conditions on $c_i$)?
