Approximate Controllability of Semilinear Impulsive Evolution Equations

Abstract EN

We prove the approximate controllability of the following semilinear impulsive evolution equation: z'=Az+Bu(t)+F(t,z,u), z∈Z, t∈(0,τ], z(0)=z0, z(tk+)=z(tk-)+Ik(tk,z(tk),u(tk)), k=1,2,3,…,p, where 0

We suppose that F is bounded and the linear system is approximately controllable on [0,δ] for all δ∈(0,τ).

Under these conditions, we prove the following statement: the semilinear impulsive evolution equation is approximately controllable on [0,τ].