Nontrivial critical groups in $p$-Laplacian problems via the Yang index
Keywordsp-Laplacian, min-max eigenvalues, Yang index, critical groups, nodal regions, p-superlinear problems
AbstractWe 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.
How to Cite
PERERA, Kanishka. Nontrivial critical groups in $p$-Laplacian problems via the Yang index. Topological Methods in Nonlinear Analysis [online]. 1 June 2003, T. 21, nr 2, s. 301–309. [accessed 7.12.2021].
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