Generic simplicity of the eigenvalues for a supported plate equation

✍ Scribed by Marcone C. Pereira

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 288 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.06.047

✦ Synopsis

In this work, we show that the eigenvalues of the problem

[
\begin{cases}\left(\Delta^{2}+V(x)+\lambda\right) u(x)=0 & x \in \Omega \ u(x)=\Delta u(x)=0 & x \in \partial \Omega\end{cases}
]

are generically simple in the set of (\mathcal{C}^{4}) regular regions of (\mathbb{R}^{n}, n \geq 2). In fact, we prove that there exists a residual set of regions (\mathcal{C}^{4}) diffeomorphic to a given (\Omega) such that all the eigenvalues for a supported plate equation are simple.