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Controllability of non-autonomous semilinear neutral equations with impulses and non-local conditions

Abstract:

In this work we study the controllability of a control system governed by a non-autonomous semilinear neutral equations with impulses and non-local conditions. The idea is to see under which conditions the controllability of the associated system of ordinary differential equations implies the controllability of the semilinear system of neutral equations with impulses and non-local conditions. This is done by imposing some conditions on the non-linear terms that appear in the system. First, we prove the approximate controllability assuming that the associated system of linear ordinary differential equations is exactly controllable over every small interval, which allows us to use a technique developed by A.E. Bashirov et al. avoiding fixed point theorems to prove approximate controllability; then assuming different conditions on the nonlinear terms of system, allows us to apply Banach Fixed Point Theorem to prove exact controllability.