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

Kanishka Perera | Zendy

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

Author(s) -

Kanishka Perera

Publication year - 2003

Publication title -

topological methods in nonlinear analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.623

H-Index - 23

ISSN - 1230-3429

DOI - 10.12775/tmna.2003.018

Subject(s) - mathematics , laplace operator , eigenvalues and eigenvectors , sequence (biology) , class (philosophy) , p laplacian , index (typography) , pure mathematics , combinatorics , mathematical analysis , computer science , artificial intelligence , world wide web , boundary value problem , physics , quantum mechanics , biology , genetics

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

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