The solution manifolds of impulsive differential equations (Q2021471)

The paper investigates the solution manifolds for the following parabolic impulsive differential equation with state-dependent delay \[ \frac{dx(t)}{dt}+Ax(t)=F(x_t), \]\[ \Delta x|_{t=t_k}=I_k(x(t_k)), \] where \(A\) is the infinitesimal generator of semigroups. The existence and uniqueness of classical solution is obtained under the assumptions that the nonlinear function and impulsive map are Lipschitz continuous.