Using Mountain Pass Theorem, the existence of weak solutions for − XN i=1 ∂ ∂xi a(x)| ∂u ∂xi |pi(x)−2 ∂u ∂xi ! = λγ(x)|u|q(x)−2u − λδ(x)|u|r(x)−2u, with Dirichlet boundary condition is studied.