Boundary value problems for highly nonlinear inclusions governed by non-surjective \(\Phi \)-Laplacians (Q632223)

The authors study various boundary value problems for the differential inclusion \[ (D(x(t))\Phi(x'(t)))'\in G(t,x(t),x'(t))\text{ a.e. }t\in I=[0,T],\tag{1} \] where \(G\) is a Carathéodory multivalued mapping with compact convex values. Neumann, Dirichlet and periodic problems, in particular, are considered. The main idea of the proofs is to reduce the considered problem to a fixed-point problem for multivalued mappings.