Nonlinear resonant degenerate equations

In this paper, we consider a degenerate Dirichlet problem with a reaction which can be resonant as [Formula: see text] with respect to the principal eigenvalue of the Dirichlet weighted [Formula: see text]-Laplacian [Formula: see text]. By using variational tools, critical groups (to overcome the fact that there is no global regularity theory for our problem) and the spectral properties of [Formula: see text], we show that problem has at least three nontrivial, bounded, ordered solutions. Two are of constant sign (positive and negative) and the third (between them) is nodal (sign-changing).