Asymmetric

We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian (a (p,2)-Laplacian) and with a reaction term,
which is superlinear in the positive direction and sublinear resonant in the negative direction. Resonance can also occur asymptotically at zero.
So, we have a double resonance situation. We establish the existence and multiplicity of nontrivial smooth solutions.