Multiple solutions for \((p, 2)\)-equations at resonance (Q1734809)

The authors study a nonlinear nonhomogeneous Dirichlet problem with a $(p,2)$-Laplacian and a reaction term $(p-1)$-linear and resonant with respect to any nonprincipal variational eigenvalue of the minus $p$-Laplacian. The main existence result provides six solutions (five of them with precise sign and order information). The first four solutions are obtained as minima of the energy functionals corresponding to appropriate truncations of the reaction term. The fifth, sign-changing, solution is obtained between the largest negative and the smallest positive ones. The last solution is provided by Morse theory.