On the solvability of systems of noncompact and nonconvex inclusions (Q5950469)

Building on the fixed point index of contractive admissible multivalued maps, the authors study existence of solutions for the system \[ y\in F(x,y),\quad x\in G(x,y) \] in a pair of Banach spaces \(X\) and \(Y\), where \(F\) \(\Omega\to 2^Y\) and \(G:\Omega\to 2^X\) \((\Omega\subseteq X\times Y)\) are upper semicontinuous. Several applications are given as well.