On the discreteness of the spectra of the Dirichlet and Neumann p -biharmonic problems

Jiří Benedikt

Abstract and Applied Analysis, 2004, vol. 2004, 1-16

Abstract:

We are interested in a nonlinear boundary value problem for ( | u ″ | p − 2 u ″ ) ′ ​ ′ = λ | u | p − 2 u in [ 0 , 1 ] , p > 1 , with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the n th eigenvalue, has precisely n − 1 zero points in ( 0 , 1 ) . Eigenvalues of the Neumann problem are nonnegative and isolated, 0 is an eigenvalue which is not simple, and the positive eigenvalues are simple and they form an increasing unbounded sequence. An eigenfunction, corresponding to the n th positive eigenvalue, has precisely n + 1 zero points in ( 0 , 1 ) .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:492348

DOI: 10.1155/S1085337504311115

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