Abstract and Applied Analysis

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

Jiří Benedikt

Full-text: Open access

Abstract

We are interested in a nonlinear boundary value problem for (|u|p2u)=λ|u|p2u 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 nth eigenvalue, has precisely n1 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 nth positive eigenvalue, has precisely n+1 zero points in (0,1).

Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 9 (2004), 777-792.

Dates
First available in Project Euclid: 10 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1097458587

Digital Object Identifier
doi:10.1155/S1085337504311115

Mathematical Reviews number (MathSciNet)
MR2102601

Zentralblatt MATH identifier
1081.34018

Subjects
Primary: 34B15: Nonlinear boundary value problems 34C10
Secondary: 47J10

Citation

Benedikt, Jiří. On the discreteness of the spectra of the Dirichlet and Neumann $p$-biharmonic problems. Abstr. Appl. Anal. 2004 (2004), no. 9, 777--792. doi:10.1155/S1085337504311115. https://projecteuclid.org/euclid.aaa/1097458587


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