Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 145, pp. 111.
Asymptotically linear fourthorder elliptic problems
whose nonlinearity crosses several eigenvalues
Evandro Monteiro
Abstract:
In this article we prove the existence of multiple solutions for
the fourthorder elliptic problem
where
is a bounded domain,
is a function
of class
such that
and it
is asymptotically linear at infinity.
We study the cases when the parameter c is less than the
first eigenvalue, and between two consecutive eigenvalues
of the Laplacian. To obtain solutions we use the Saddle Point Theorem,
the Linking Theorem, and Critical Groups Theory.
Submitted February 15, 2011. Published November 2, 2011.
Math Subject Classifications: 35J30, 35J35.
Key Words: Asymptotically linear; Morse theory; shifting theorem;
multiplicity of solutions.
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Evandro Monteiro
UNIFALMG, Rua Gabriel Monteiro da Silva, 700. Centro
CEP 37130000 AlfenasMG, Brazil
email: evandromonteiro@unifalmg.edu.br

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