We study in this chapter the following nonlinear elliptic boundary value problem,
b(u)−diva(x,u,∇u)=fin Ω,a(x,u,∇u).η=−|u|r(x,u)−2uon ∂Ω,
where Ω is a bounded open domain in ℝN, N≥3, with smooth boundary ∂Ω. We prove the existence and uniqueness of weak solution for f∈L1(Ω) and structural stability result.

p(u)-Laplacian; Young measure; Robin boundary condition; existence and uniqueness