Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators

Abstract

In this article, we prove the existence and uniqueness of solutions for the Navier problem(P)∆ω(x)(|∆u|p−2∆u + |∆u|q−2∆u)− divω(x)(|∇u|p−2∇u + |∇u|q−2∇u)= f(x) − div(G(x)), in Ω,u(x) = ∆u = 0, in ∂Ω,where Ω is a bounded open set of RN (N ≥ 2), fω∈Lp0(Ω, ω) and Gω∈ [Lq0(Ω, ω)]N .