Approximate controllability of a coupled nonlocal partial functional integro-differential equations with impulsive effects (Q6580047)

In this paper, the authors study the approximate controllability problem for a system governed by the integro-differential equation with impulsive effects and nonlocal initial conditions. They firstly investigate the existence and uniqueness of solutions for the referenced system by the theory of resolvent operators combined with fixed point theory in a generalized Banach space. They secondly study the approximate controllability of the reference system without necessarily requiring the nonlinear terms to be uniformly bounded. Particularly, by the generalized measure of noncompactness, the compactness condition for the resolvent operator and the state-dependent function in the nonlocal condition is dropped, which is commonly found in some known results. Finally, they provide an example to demonstrate the abstract results of this work.