Boundary value problems for strongly nonlinear multivalued equations involving different $Phi$-Laplacians

We investigate the existence of solutions to the scalar differential inclusion (D(x(t))Phi(x'(t)))' is an element of G(t, x(t), x' (t) a.e. t is an element of I = [0, T] , where D(x) is a positive and continuous function., G(t, x, x') is a Caratheodory multifunction and the increasing homeomorphism Phi can have a bounded domain of the type (-a, a) or it can be the p-Laplacian operator. Using fixed-point techniques combined, in some cases, with the method of lower and upper solutions, we prove the existence of solutions satisfying various boundary conditions.