Strong convergence of solutions of nonlinear Volterra equations in Banach spaces (Q2757175)

The author studies the convergence of the solution \(u\) of the equation NEWLINE\[NEWLINE u(t)+ \int_0^t b(t-s) (Au(s) + g(s)u(s)) ds \ni f(t),\quad t\geq 0, NEWLINE\]NEWLINE in a real Banach space \(X\) where \(A\) is an \(m\)-accretive operator, \(b\) is a completely positive kernel, and \(g\in L^1(\mathbb{R}^+)\). It is shown that under certain assumptions on the function \(f\) the solution \(u\) converges to a limit as \(t\to \infty\).