We consider Dirichlet elliptic equations driven by the sum of a ▫$p$▫-Laplacian ▫$(2<p)$▫ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both ▫$\pm ...\infty$▫ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.
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