Existence for neutral impulsive differential inclusions with nonlocal conditions (Q927939)

The paper deals with nonlocal impulsive Cauchy problems governed by semilinear neutral functional differential inclusions. First, the existence of solutions for the following system in a Banach space \(X\) is studied: \[ \frac{d}{dt}\left[x(t)-F(t,x(h_1(t)))\right]\in\, -Ax(t)\, +\, G(t,x(h_2(t)))\, ,\;t\in [0,a],\;t\neq t_k,\;k=1,\dots, m, \] \[ \Delta x| _{t=t_k}=I_k(x(t_k^-))\, ,\;k=1,\dots,m, \] \[ x(0)+g(x)=x_0\in X, \] where \(-A\) is the infinitesimal generator of a compact analytic semigroup; \(G\) is a multivalued map; \(\Delta x| _{t=t_k}=x(t_k^+)-x(t_k^-)\); \(0=t_0<t_1<\dots <t_m<t_{m+1}=a\); \(F,\, h_1,\, h_2,\, I_k,\, g\) are given functions. Then, an example is presented to illustrate the applications of the existence results.