2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104809We establish existence and multiplicity theorems for a Dirichlet boundary value problem at resonance, which is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta. Our framework includes a sign-changing potential and we locate the solutions by using the Mountain Pass lemma and the Saddle Point theorem.Analysis of PDEsMathematical Physics35A15, 35J60, 35P30, 58E05text