Existence and solution sets of impulsive functional differential inclusions with multiple delay (Q2901950)

The authors present some existence results of solutions and study the topological structure of the solution sets for the first-order impulsive neutral functional differential inclusion NEWLINE\[NEWLINE\frac{d}{dt}[y(t)-g(t,y_t)]\in F(t,y_t)+\sum\limits_{i=1}^{n}y(t-T_i) \text{ for a.e. } t\in {J\{t_1,\dotsc,t_m\}},NEWLINE\]NEWLINE NEWLINE\[NEWLINEy(t_k^+)-y(t_k^-)=I_k(y(t_k^-)),\;k=1,\dotsc,m,NEWLINE\]NEWLINE NEWLINE\[NEWLINEy(t)=\phi (t), \;t\in [-r,0],NEWLINE\]NEWLINE where \(J=[0,b]\) and \(0=t_0<t_1<\dotsb<t_m<t_{m+1}=b\), \(F\) is a set-valued map and \(g\) is single-valued. The functions \(I_k\) characterize the jump of the solutions at the impulse points \(t_k\) \((k=1,\dotsc,m)\).