Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay (Q1022815)

The authors study the existence of solutions for the following differential inclusion in a Banach space on finite and infinite intervals: \[ y'(t)\in A(t)y(t)+F(t,y_t),\quad t\neq t_k, t\geq 0, \] \[ y(t)=x(t), t\in [-\tau,0],\quad y(t_k^+)=y(t_k)+I_k(y(t_k)), \] where \(A(t)\) is not necessarily a bounded linear operator. For infinite intervals the results obtained in the paper are new even in the non-impulsive case.