Solvability of nonlinear impulsive Volterra integral inclusions and functional differential inclusions (Q596727)

The author applies his fixed point theorem [J. Math. Anal. App1. 282, No. 1, 151--162 (2003; Zbl 1051.47042)] to obtain existence of solutions for the nonlinear impulsive Volterra inclusion of the form \[ x(t)= h(t)+ \int^t_0 f_x(t,s)\,ds+ \sum_{0< t_k< t} a_k(t) I_k(x(t_k)),\quad t\in J. \] Here \(x\) takes values in a partially ordered Banach space, \(h\) is piecewise continuous, \(f_x\in L^1(J\times J,E)\) is an \(L^1\)-selection of a multivalued map \(F\), \(a_k\in L^1([t_k, a], R_+)\) and \(I_k\in C(E, E)\), \(k= 1,\dots, m\). The result is applied to certain second-order impulsive multivalued functional differential inclusions.