Eigenfunctions for rectangles with Neumann boundary conditions

Abstract

Consider the eigenfunctions $u$ for a ree rectangular membrane wo that $-\Delta u=\lambda u$ on $\mathcal{R}(c,d)=(0,d)\times (0,d)$. In this note we show that if if $u>0$ on $\partial \mathcal{R}(c,d))then$u\equiv C$ for some positive constant.

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