Internal nonlocal and integral condition problems of the differential equation (x = f(t; x; x ))

In this work, we are concerned with the existence of at least one absolutely continuous solution of the Cauchy problem for the differential equation (x = f(t; x; x ), t in (0; 1)) with the internal nonlocal condition m (sum^m_{k=1} a_kx(tau_k) = x_o, tau_k in (c, d) subseteq (0; 1)). The problem of the integral condition (int^d_c x(s) dg(s) = x_o) will be considered.