Multiple solutions for nearly resonant nonlinear Dirichlet problems

In this paper we consider parametric nonlinear elliptic problems driven by the p-Laplacian differential operator and with the parameter $\lambda$ near $\lambda_1$, the principal eigenvalue of the negative Dirichlet p-Laplacian (near resonance). We consider both cases when $\lambda < \lambda_1$ (near resonance from the left) and when $\lambda > \lambda_1$ (near resonance from the right). Our approach combines variational methods based on the critical point theory, together with truncation techniques and Morse theory.