Boundary value problems for discontinuous perturbations of singular ϕ-Laplacian operator

Systems of differential inclusions of the form−(ϕ(u′))′∈∂F(t,u),t∈[0,T], where ϕ=∇Φϕ=∇Φ, with Φ strictly convex, is a homeomorphism of the ball Ba⊂RNBa⊂RN onto RNRN, are considered under Dirichlet, periodic and Neumann boundary conditions. Here, ∂F(t,x)∂F(t,x) stands for the generalized Clarke gradient of F(t,⋅)F(t,⋅) at x∈RNx∈RN. Using nonsmooth critical point theory, we obtain existence results under some appropriate conditions on the potential F. Examples of applications concerning Filippov type solutions are also provided.