We consider a nonlinear nonhomogeneous Dirichlet problem driven
by the sum of a p−Laplacian and a Laplacian (a (p, 2)− equation). The reaction
is the sum of two competing terms, a parametric (p − 1)−sublinear term and
an asymmetric (p − 1)−linear perturbation which is resonant at −∞. Using
variational methods together with truncations and comparison techniques and
Morse theory (critical groups), we prove two multiplicity theorems which provide
sign information for all the solutions.publishe
