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

Kanishka Perera

DOI: http://dx.doi.org/10.12775/TMNA.2003.018

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.

Keywords


p-Laplacian; min-max eigenvalues; Yang index; critical groups; nodal regions; p-superlinear problems

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