On some nonlocal eigenvalue problems | Zendy

Ravi P. Agarwal | Zendy; Kanishka Perera | Zendy; Zhitao Zhang | Zendy

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On some nonlocal eigenvalue problems

Author(s) -

Ravi P. Agarwal,

Kanishka Perera,

Zhitao Zhang

Publication year - 2011

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 34

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2012.5.707

Subject(s) - minimax , eigenvalues and eigenvectors , mathematics , multiplicity (mathematics) , boundary value problem , class (philosophy) , morse code , scheme (mathematics) , pure mathematics , sequence (biology) , mathematical analysis , mathematical optimization , physics , computer science , quantum mechanics , telecommunications , artificial intelligence , biology , genetics

We study a class of nonlocal eigenvalue problems related to certain boundary value problems that arise in many application areas. We construct a nondecreasing and unbounded sequence of eigenvalues that yields nontrivial critical groups for the associated variational functional using a nonstandard minimax scheme that involves the $\mathbb{Z}_2$-cohomological index. As an application we prove a multiplicity result for a class of nonlocal boundary value problems using Morse theory.

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