Global existence results for first-order integrodifferential identification problems (Q1356821)

Sufficient conditions on the linear operators \(A, H, H_0\) are established under which any solution \(u\) to the integrodifferential equation \[ u(t)= Au(t)+ \int_0^t H(t- s)Au(s)ds+ \int_0^t H_0(t-s)u(s)ds+ g(t) \tag{1} \] is positive if the pair \((g,u(0))\) is positive. Sufficient conditions for the uniqueness of the solution to the equation (1) with \(g(t)= E(t)z+f(t)\) are also given and the existence in large of a unique solution is proved.