Consider the Volterra integral equation $$ f(t) = g(t) +\int_0^t K(t,s) f(s) ds $$ where $g(t)$ is continuous on $t\in[0,T]$ and $K(t,s)$ is a weakly singular kernel. It is well known that there exists a unique continuous solution $f(t)$.
Can we extend the above existence theorem for one dimensional linear Volterra integral equation to a system of linear Volterra equations?