Exact controllability of generalized Hammerstein type integral equation and applications

Abstract

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation x(t) = ∫t0 h(t, s)u(s)ds + ∫t0k(t, s, x)ƒ(s, x(s))ds, 0 ≤ t ≤ T < ∞, where, the state x(t) lies in a Hilbert space H and control u(t) lies another Hilbert space V for each time t ∈ I = [0, T], T > 0. We establish the controllability result under suitable assumptions on h, k and ƒ using the monotone operator theory.