Nonresonance impulsive functional differential inclusions with variable times
The authors study the existence of solutions of a boundary value problem for first-order functional-differential inclusions with state dependent impulses of the type \[ y'(t)-\lambda y(t)\in F(t,y_t),\text{ for a.e. } t\in J=[0,T]\setminus \{t_1(y(t)),\dots, t_m(y(t))\}, \] \[ y(t^{+}) =I_k(y(t^-)), t=t_k(y(t)), k=1,\dots, m, \] \[ y(t)=\varphi(t), t\in [-r,0], y(0)=y(T), \] and a similar second-order problem. The proof of the main result is based on Martelli's fixed-point theorem for condensing multivalued maps.
impulsive functional-differential inclusions
scientific article; zbMATH DE number 2142423
scientific article