Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 492348 | https://doi.org/10.1155/S1085337504311115

Jiří Benedikt, "On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems", Abstract and Applied Analysis, vol. 2004, Article ID 492348, 16 pages, 2004. https://doi.org/10.1155/S1085337504311115

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

Received15 Aug 2003

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).

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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