Nonlinear multivalued homogeneous Robin boundary p(u)-laplacian problem

We study the following nonlinear multivalued Robin boundary p(u)− laplacian problem β(u) − diva(x, u, ∇u) ∋ f in Ω, a(x, u, ∇u).η = −|u|r(x,u)−2u on ∂Ω. The existence and uniqueness of solutions for L1-data f are established.