On a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general Banach spaces ✩

Sufficient conditions on the existence of mild solutions for the following semilinear nonlocal evolution inclusion with upper semicontinuous nonlinearity: u (t) ∈ A(t)u(t) + F(t,u(t)), 0 < t d, u(0) = g(u), are given when g is completely continuous and Lipschitz continuous in general Banach spaces, respectively. An example concerning the partial differential equation is also presented. © 2007 Elsevier Inc. All rights reserved