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 -biharmonic problems
We are interested in a nonlinear boundary value problem for in , , 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 th eigenvalue, has precisely zero points in . Eigenvalues of the Neumann problem are nonnegative and isolated, 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 th positive eigenvalue, has precisely zero points in .
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