Nontrivial critical groups in $p$-Laplacian problems via the Yang index

Abstract

We construct and variationally characterize by a min-max procedure involving the Yang index a new sequence of eigenvalues of the $p$-Laplacian, and use the structure provided by this sequence to show that the associated variational functional always has a nontrivial critical group. As an application we obtain nontrivial solutions for a class of $p$-superlinear problems.