A method of upper and lower solutions for functional differential inclusions. (Q1872627)

The authors establish the existence of solutions for a class of functional-differential inclusions described in the form \[ \dot{x}(t)\in \,\,F(t,x_{t}), \;t\geq\sigma, \quad x_{\sigma}=\varphi,\;varphi\in C([-r,0]:\mathbb{R}), \] where \(F:J\times C([-r,0]:\mathbb{R})\to 2^{\mathbb{R}}\) is a compact and convex multivalued map. The main result is proved using a fixed-point theorem for condensing operators.