Multiple solutions for perturbed quasilinear elliptic problems

We investigate the existence of multiple solutions for the (p q)-quasilinear elliptic problem {-Delta(p)u - Delta(q)u = g(x; u) + epsilon h(x, u) in Omega u = 0 on partial derivative Omega where 1 < p < q < +infinity, Omega is an open bounded domain of R-N, the non-linearity g(x, u) behaves at infinity as vertical bar u vertical bar(q-1), epsilon is an element of R and h is an element of C(<(Omega)over bar> x R, R). In spite of the possible lack of a variational structure of this problem, from suitable assumptions on g(x, u) and appropriate procedures and estimates, the existence of multiple solutions can be proved for small perturbations.