On the solvability of systems of non-convex inclusions in Banach spaces (Q1191395)

The paper starts with a general description of the topological degree theory for a special class of set-valued maps, called admissible. The main result is that the authors state sufficient conditions for the existence of solutions of the system: \(0\in\phi(x,y)\wedge 0\in\psi(x,y)\), where \(\phi,\psi\) are admissible maps defined on a subset of the cartesian product of two normed spaces. The main tool is Dold's technique to investigate fixed points of fiber-preserving maps. Some applications concerning periodic solutions of differential systems are given.